MPSEnvironment¶

full name: tenpy.networks.mps.MPSEnvironment
parent module: tenpy.networks.mps
type: class

Inheritance Diagram

Methods

`MPSEnvironment.__init__`(bra, ket[, cache])
`MPSEnvironment.cache_optimize`([...])	Update short_term_keys for the cache and possibly preload tensors.
`MPSEnvironment.clear`()	Delete all partial contractions except the left-most LP and right-most RP.
`MPSEnvironment.correlation_function`(ops1, ops2)	Correlation function `<bra\|op1_i op2_j\|ket>` of single site operators, sandwiched between bra and ket. For examples the contraction for a two-site operator on site i would look like::.
`MPSEnvironment.del_LP`(i)	Delete stored part strictly to the left of site i.
`MPSEnvironment.del_RP`(i)	Delete stored part scrictly to the right of site i.
`MPSEnvironment.expectation_value`(ops[, ...])	Expectation value `<bra\|ops\|ket>` of (n-site) operator(s).
`MPSEnvironment.expectation_value_multi_sites`(...)	Expectation value `<bra\|op0_{i0}op1_{i0+1}...opN_{i0+N}\|ket>`.
`MPSEnvironment.expectation_value_term`(term)	Expectation value `<bra\|op_{i0}op_{i1}...op_{iN}\|ket>`.
`MPSEnvironment.expectation_value_terms_sum`(...)	Calculate expectation values for a bunch of terms and sum them up.
`MPSEnvironment.full_contraction`(i0)	Calculate the overlap by a full contraction of the network.
`MPSEnvironment.get_LP`(i[, store])	Calculate LP at given site from nearest available one.
`MPSEnvironment.get_LP_age`(i)	Return number of physical sites in the contractions of get_LP(i).
`MPSEnvironment.get_RP`(i[, store])	Calculate RP at given site from nearest available one.
`MPSEnvironment.get_RP_age`(i)	Return number of physical sites in the contractions of get_RP(i).
`MPSEnvironment.get_initialization_data`([...])	Return data for (re-)initialization of the environment.
`MPSEnvironment.get_op`(op_list, i)	Given a list of operators, select the one corresponding to site i.
`MPSEnvironment.has_LP`(i)	Return True if LP left of site i is stored.
`MPSEnvironment.has_RP`(i)	Return True if RP right of site i is stored.
`MPSEnvironment.init_LP`(i[, start_env_sites])	Build initial left part `LP`.
`MPSEnvironment.init_RP`(i[, start_env_sites])	Build initial right part `RP` for an MPS/MPOEnvironment.
`MPSEnvironment.init_first_LP_last_RP`([...])	(Re)initialize first LP and last RP from the given data.
`MPSEnvironment.set_LP`(i, LP, age)	Store part to the left of site i.
`MPSEnvironment.set_RP`(i, RP, age)	Store part to the right of site i.
`MPSEnvironment.term_correlation_function_left`(...)	Correlation function between (multi-site) terms, moving the left term, fix right term.
`MPSEnvironment.term_correlation_function_right`(...)	Correlation function between (multi-site) terms, moving the right term, fix left term.
`MPSEnvironment.term_list_correlation_function_right`(...)	Correlation function between sums of multi-site terms, moving the right sum of term.
`MPSEnvironment.test_sanity`()	Sanity check, raises ValueErrors, if something is wrong.

class tenpy.networks.mps.MPSEnvironment(bra, ket, cache=None, **init_env_data)[source]¶

Bases: BaseEnvironment, BaseMPSExpectationValue

Class storing partial contractions between two different MPS and providing expectation values.

The network for a contraction \(<bra|Op|ket>\) of a local operator Op, say exemplary at sites i, i+1 looks like:

|     .-----M[0]--- ... --M[1]---M[2]--- ... ->--.
|     |     |             |      |               |
|     |     |             |------|               |
|     LP[0] |             |  Op  |               RP[-1]
|     |     |             |------|               |
|     |     |             |      |               |
|     .-----N[0]*-- ... --N[1]*--N[2]*-- ... -<--.

This class stores the partial contractions LP and RP coming from the left and right up to each bond, allowing efficient calculations of expectation values, correlation functions etc.

We use the following label convention (where arrows indicate qconj):

|    .-->- vR           vL ->-.
|    |                        |
|    LP                       RP
|    |                        |
|    .--<- vR*         vL* -<-.

full_contraction(i0)[source]¶

Calculate the overlap by a full contraction of the network.

The full contraction of the environments gives the overlap <bra|ket>, taking into account the MPS.norm of both bra and ket. For this purpose, this function contracts get_LP(i0+1, store=False) and get_RP(i0, store=False) with appropriate singular values in between.

Parameters: i0 (int) – Site index.

cache_optimize(short_term_LP=[], short_term_RP=[], preload_LP=None, preload_RP=None)[source]¶

Update short_term_keys for the cache and possibly preload tensors.

Parameters

short_term_LP (list of int) – i indices for get_LP() and get_RP(), respectively, for which a repeated look-up could happen, i.e., for which tensors should be kept in RAM until the next call to this function.
short_term_RP (list of int) – i indices for get_LP() and get_RP(), respectively, for which a repeated look-up could happen, i.e., for which tensors should be kept in RAM until the next call to this function.
preload_LP (int | None) – If not None, preload the tensors for the corrsponding get_LP() and get_RP() call, respectively, from disk.
preload_RP (int | None) – If not None, preload the tensors for the corrsponding get_LP() and get_RP() call, respectively, from disk.

clear()[source]¶: Delete all partial contractions except the left-most LP and right-most RP.

correlation_function(ops1, ops2, sites1=None, sites2=None, opstr=None, str_on_first=True, hermitian=False, autoJW=True)[source]¶

Correlation function <bra|op1_i op2_j|ket> of single site operators, sandwiched between bra and ket. For examples the contraction for a two-site operator on site i would look like:

|          .--S--B[i]--B[i+1]--...--B[j]---.
|          |     |     |            |      |
|          |     |     |            op2    |
|          LP[i] |     |            |      RP[j]
|          |     op1   |            |      |
|          |     |     |            |      |
|          .--S--B*[i]-B*[i+1]-...--B*[j]--.

Onsite terms are taken in the order <psi | op1 op2 | psi>. If opstr is given and str_on_first=True, it calculates:

|           for i < j                               for i > j
|
|          .--S--B[i]---B[i+1]--...- B[j]---.     .--S--B[j]---B[j+1]--...- B[i]---.
|          |     |      |            |      |     |     |      |            |      |
|          |     opstr  opstr        op2    |     |     op2    |            |      |
|          LP[i] |      |            |      RP[j] LP[j] |      |            |      RP[i]
|          |     op1    |            |      |     |     opstr  opstr        op1    |
|          |     |      |            |      |     |     |      |            |      |
|          .--S--B*[i]--B*[i+1]-...- B*[j]--.     .--S--B*[j]--B*[j+1]-...- B*[i]--.

For i==j, no opstr is included. For str_on_first=False, the opstr on site min(i, j) is always left out. Strings (like 'Id', 'Sz') in the arguments are translated into single-site operators defined by the Site on which they act. Each operator should have the two legs 'p', 'p*'.

Warning

This function is only evaluating correlation functions by moving right, and hence can be inefficient if you try to vary the left end while fixing the right end. In that case, you might be better off (=faster evaluation) by using term_correlation_function_left() with a small for loop over the right indices.

Parameters

ops1 ((list of) { Array | str }) – First operator of the correlation function (acting after ops2). If a list is given, ops1[i] acts on site i of the MPS. Note that even if a list is given, we still just evaluate two-site correlations! psi.correlation_function(['A','B'], ['C', 'D']) evaluates <A_i C_j> for even i and even j, <B_i C_j> for even i and odd j, <B_i C_j> for odd i and even j, and <B_i D_j> for odd i and odd j.
ops2 ((list of) { Array | str }) – Second operator of the correlation function (acting before ops1). If a list is given, ops2[j] acts on site j of the MPS.
sites1 (None | int | list of int) – List of site indices i; a single int is translated to range(0, sites1). None defaults to all sites range(0, L). Is sorted before use, i.e. the order is ignored.
sites2 (None | int | list of int) – List of site indices; a single int is translated to range(0, sites2). None defaults to all sites range(0, L). Is sorted before use, i.e. the order is ignored.
opstr (None | (list of) { Array | str }) – Ignored by default (None). Operator(s) to be inserted between ops1 and ops2. If less than L operators are given, we repeat them periodically. If given as a list, opstr[r] is inserted at site r (independent of sites1 and sites2).
str_on_first (bool) – Whether the opstr is included on the site min(i, j). Note the order, which is chosen that way to handle fermionic Jordan-Wigner strings correctly. (In other words: choose str_on_first=True for fermions!)
hermitian (bool) – Optimization flag: if sites1 == sites2 and Ops1[i]^\dagger == Ops2[i] (which is not checked explicitly!), the resulting C[x, y] will be hermitian. We can use that to avoid calculations, so hermitian=True will run faster.
autoJW (bool) – Ignored if opstr is given. If True, auto-determine if a Jordan-Wigner string is needed. Works only if exclusively strings were used for op1 and op2.

Returns

C – The correlation function C[x, y] = <bra|ops1[i] ops2[j]|ket>, where ops1[i] acts on site i=sites1[x] and ops2[j] on site j=sites2[y]. If opstr is given, it gives (for str_on_first=True): - For i < j: C[x, y] = <bra|ops1[i] prod_{i <= r < j} opstr[r] ops2[j]|ket>. - For i > j: C[x, y] = <bra|prod_{j <= r < i} opstr[r] ops1[i] ops2[j]|ket>. - For i = j: C[x, y] = <bra|ops1[i] ops2[j]|ket>. The condition <= r is replaced by a strict < r, if str_on_first=False.

Warning

The MPSEnvironment variant of this method takes the accumulated MPS norm into account, which is non-trivial e.g. when you used apply_local_op with non-unitary operators.

In contrast, the MPS variant of this method ignores the norm, i.e. returns the expectation value for the normalized state.

Return type

2D ndarray

Examples

Let’s prepare a state in alternating |+z>, |+x> states:

>>> spin_half = tenpy.networks.site.SpinHalfSite(conserve=None)
>>> p_state = ['up', [np.sqrt(0.5), -np.sqrt(0.5)]]*3
>>> psi = tenpy.networks.mps.MPS.from_product_state([spin_half]*6, p_state, "infinite")

Default arguments calculate correlations for all i and j within the MPS unit cell. To evaluate the correlation function for a single i, you can use sites1=[i]. Alternatively, you can use term_correlation_function_right() (or term_correlation_function_left()):

>>> psi.correlation_function("Sz", "Sx")  
array([[ 0.  , -0.25,  0.  , -0.25,  0.  , -0.25],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  , -0.25,  0.  , -0.25,  0.  , -0.25],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  , -0.25,  0.  , -0.25,  0.  , -0.25],
       [ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  0.  ]])
>>> psi.correlation_function("Sz", "Sx", [0])
array([[ 0.  , -0.25,  0.  , -0.25,  0.  , -0.25]])
>>> corr1 = psi.correlation_function("Sz", "Sx", [0], range(1, 10))
>>> corr2 = psi.term_correlation_function_right([("Sz", 0)], [("Sx", 0)], 0, range(1, 10))
>>> assert np.all(np.abs(corr2 - corr1) < 1.e-12)

For fermions, it auto-determines that/whether a Jordan Wigner string is needed:

>>> fermion = tenpy.networks.site.FermionSite(conserve='N')
>>> p_state = ['empty', 'full'] * 3
>>> psi = tenpy.networks.mps.MPS.from_product_state([fermion]*6, p_state, "finite")
>>> CdC = psi.correlation_function("Cd", "C")  # optionally: use `hermitian=True`
>>> psi.correlation_function("C", "Cd")[1, 2] == -CdC[2, 1]
True
>>> np.all(np.diag(CdC) == psi.expectation_value("Cd C"))  # "Cd C" is equivalent to "N"
True

See also

expectation_value_term: for a single combination of i and j of A_i B_j`.
term_correlation_function_right: for correlations between multi-site terms, fix left term.
term_correlation_function_left: for correlations between multi-site terms, fix right term.

del_LP(i)[source]¶: Delete stored part strictly to the left of site i.

del_RP(i)[source]¶: Delete stored part scrictly to the right of site i.

expectation_value(ops, sites=None, axes=None)[source]¶

Expectation value <bra|ops|ket> of (n-site) operator(s).

Calculates n-site expectation values of operators sandwiched between bra and ket. For examples the contraction for a two-site operator on site i would look like:

|          .--S--B[i]--B[i+1]--.
|          |     |     |       |
|          |     |-----|       |
|          LP[i] | op  |       RP[i+1]
|          |     |-----|       |
|          |     |     |       |
|          .--S--B*[i]-B*[i+1]-.

Here, the B are taken from ket, the B* from bra. For MPS expectation values these are the same and LP/ RP are trivial.

Parameters

ops ((list of) { Array | str }) – The operators, for wich the expectation value should be taken, All operators should all have the same number of legs (namely 2 n). If less than len(sites) operators are given, we repeat them periodically. Strings (like 'Id', 'Sz') are translated into single-site operators defined by sites.
sites (list) – List of site indices. Expectation values are evaluated there. If None (default), the entire chain is taken (clipping for finite b.c.)
axes (None | (list of str, list of str)) – Two lists of each n leg labels giving the physical legs of the operator used for contraction. The first n legs are contracted with conjugated B, the second n legs with the non-conjugated B. None defaults to (['p'], ['p*']) for single site (n=1), or (['p0', 'p1', ... 'p{n-1}'], ['p0*', 'p1*', .... 'p{n-1}*']) for n > 1.

Returns

exp_vals – Expectation values, exp_vals[i] = <bra|ops[i]|ket>, where ops[i] acts on site(s) j, j+1, ..., j+{n-1} with j=sites[i].

Warning

The MPSEnvironment variant of this method takes the accumulated MPS norm into account, which is non-trivial e.g. when you used apply_local_op with non-unitary operators.

In contrast, the MPS variant of this method ignores the norm, i.e. returns the expectation value for the normalized state.

Return type

1D ndarray

Examples

Let’s prepare a state in alternating |+z>, |+x> states:

>>> spin_half = tenpy.networks.site.SpinHalfSite(conserve=None)
>>> p_state = ['up', [np.sqrt(0.5), -np.sqrt(0.5)]]*3
>>> psi = tenpy.networks.mps.MPS.from_product_state([spin_half]*6, p_state)

One site examples (n=1):

>>> Sz = psi.expectation_value('Sz')
>>> print(Sz)
[0.5 0.  0.5 0.  0.5 0. ]
>>> Sx = psi.expectation_value('Sx')
>>> print(Sx)
[ 0.  -0.5  0.  -0.5  0.  -0.5]
>>> print(psi.expectation_value(['Sz', 'Sx']))
[ 0.5 -0.5  0.5 -0.5  0.5 -0.5]
>>> print(psi.expectation_value('Sz', sites=[0, 3, 4]))
[0.5 0.  0.5]

Two site example (n=2), assuming homogeneous sites:

>>> SzSx = npc.outer(psi.sites[0].Sz.replace_labels(['p', 'p*'], ['p0', 'p0*']),
...                  psi.sites[1].Sx.replace_labels(['p', 'p*'], ['p1', 'p1*']))
>>> print(psi.expectation_value(SzSx))  # note: len L-1 for finite bc, or L for infinite
[-0.25  0.   -0.25  0.   -0.25]

Example measuring <psi|SzSx|psi> on each second site, for inhomogeneous sites:

>>> SzSx_list = [npc.outer(psi.sites[i].Sz.replace_labels(['p', 'p*'], ['p0', 'p0*']),
...                        psi.sites[i+1].Sx.replace_labels(['p', 'p*'], ['p1', 'p1*']))
...              for i in range(0, psi.L-1, 2)]
>>> print(psi.expectation_value(SzSx_list, range(0, psi.L-1, 2)))
[-0.25 -0.25 -0.25]

Expectation value with different bra and ket in an MPSEnvironment:

>>> spin_half = tenpy.networks.site.SpinHalfSite(conserve=None)
>>> p2_state = [[np.sqrt(0.5), -np.sqrt(0.5)], 'up']*3
>>> phi = tenpy.networks.mps.MPS.from_product_state([spin_half]*6, p2_state)
>>> env = tenpy.networks.mps.MPSEnvironment(phi, psi)
>>> Sz = env.expectation_value('Sz')
>>> print(Sz)
[0.0625 0.0625 0.0625 0.0625 0.0625 0.0625]

expectation_value_multi_sites(operators, i0)[source]¶

Expectation value <bra|op0_{i0}op1_{i0+1}...opN_{i0+N}|ket>.

Calculates the expectation value of a tensor product of single-site operators acting on different sites next to each other. In other words, evaluate the expectation value of a term op0_i0 op1_{i0+1} op2_{i0+2} ..., looking like this (with op short for operators, for len(operators)=3):

|          .--S--B[i0]---B[i0+1]--B[i0+2]--B[i0+3]--.
|          |     |       |        |        |        |
|         LP[i0] op[0]   op[1]    op[2]    op[3]    RP[i0+3]
|          |     |       |        |        |        |
|          .--S--B*[i0]--B*[i0+1]-B*[i0+2]-B*[i0+3]-.

Warning

This function does not automatically add Jordan-Wigner strings! For correct handling of fermions, use expectation_value_term() instead.

Parameters

operators (List of { Array | str }) – List of one-site operators. This method calculates the expectation value of the n-sites operator given by their tensor product.
i0 (int) – The left most index on which an operator acts, i.e., operators[i] acts on site i + i0.

Returns

exp_val – The expectation value of the tensorproduct of the given onsite operators, <bra|operators[0]_{i0} operators[1]_{i0+1} ... |ket>.

Warning

The MPSEnvironment variant of this method takes the accumulated MPS norm into account, which is non-trivial e.g. when you used apply_local_op with non-unitary operators.

In contrast, the MPS variant of this method ignores the norm, i.e. returns the expectation value for the normalized state.

Return type

float/complex

expectation_value_term(term, autoJW=True)[source]¶

Expectation value <bra|op_{i0}op_{i1}...op_{iN}|ket>.

Calculates the expectation value of a tensor product of single-site operators acting on different sites i0, i1, … (not necessarily next to each other). In other words, evaluate the expectation value of a term op0_i0 op1_i1 op2_i2 ....

For example the contraction of three one-site operators on sites i0, i1=i0+1, i2=i0+3 would look like:

|          .--S--B[i0]---B[i0+1]--B[i0+2]--B[i0+3]--.
|          |     |       |        |        |        |
|         LP[i0]op1     op2       |       op3       RP[i0+3]
|          |     |       |        |        |        |
|          .--S--B*[i0]--B*[i0+1]-B*[i0+2]-B*[i0+3]-.

Parameters

term (list of (str, int)) – List of tuples op, i where i is the MPS index of the site the operator named op acts on. The order inside term determines the order in which they act (in the mathematical convention: the last operator in term is right-most, so it acts first on a ket).
autoJW (bool) – If True (default), automatically insert Jordan Wigner strings for Fermions as needed.

Returns

exp_val – The expectation value of the tensorproduct of the given onsite operators, <bra|op_i0 op_i1 ... op_iN |ket>.

Warning

The MPSEnvironment variant of this method takes the accumulated MPS norm into account, which is non-trivial e.g. when you used apply_local_op with non-unitary operators.

In contrast, the MPS variant of this method ignores the norm, i.e. returns the expectation value for the normalized state.

Return type

float/complex

See also

correlation_function: efficient way to evaluate many correlation functions.

Examples

>>> a = psi.expectation_value_term([('Sx', 2), ('Sz', 4)])
>>> b = psi.expectation_value_term([('Sz', 4), ('Sx', 2)])
>>> c = psi.expectation_value_multi_sites(['Sz', 'Id', 'Sx'], i0=2)
>>> assert a == b == c

expectation_value_terms_sum(term_list)[source]¶

Calculate expectation values for a bunch of terms and sum them up.

This is equivalent to the following expression:

sum([self.expectation_value_term(term)*strength for term, strength in term_list])

However, for effiency, the term_list is converted to an MPO and the expectation value of the MPO is evaluated.

Warning

This function works only for finite bra and ket and does not include normalization factors.

Parameters

term_list (TermList) – The terms and prefactors (strength) to be summed up.

Returns

terms_sum (list of (complex) float) – Equivalent to the expression sum([self.expectation_value_term(term)*strength for term, strength in term_list]).
_mpo – Intermediate results: the generated MPO. For a finite MPS, terms_sum = _mpo.expectation_value(self), for an infinite MPS terms_sum = _mpo.expectation_value(self) * self.L

See also

expectation_value_term: evaluates a single term.
tenpy.networks.mpo.MPO.expectation_value: expectation value density of an MPO.

get_LP(i, store=True)[source]¶

Calculate LP at given site from nearest available one.

The returned LP_i corresponds to the following contraction, where the M’s and the N’s are in the ‘A’ form:

|     .-------M[0]--- ... --M[i-1]--->-   'vR'
|     |       |             |
|     LP[0]   |             |
|     |       |             |
|     .-------N[0]*-- ... --N[i-1]*--<-   'vR*'

Parameters

i (int) – The returned LP will contain the contraction strictly left of site i.
store (bool) – Whether to store the calculated LP in self (True) or discard them (False).

Returns

LP_i – Contraction of everything left of site i, with labels 'vR*', 'vR' for bra, ket.

Return type

Array

get_LP_age(i)[source]¶

Return number of physical sites in the contractions of get_LP(i).

Might be None.

get_RP(i, store=True)[source]¶

Calculate RP at given site from nearest available one.

The returned RP_i corresponds to the following contraction, where the M’s and the N’s are in the ‘B’ form:

|     'vL'  ->---M[i+1]-- ... --M[L-1]----.
|                |              |         |
|                |              |         RP[L-1]
|                |              |         |
|     'vL*' -<---N[i+1]*- ... --N[L-1]*---.

Parameters

i (int) – The returned RP will contain the contraction strictly right of site i.
store (bool) – Whether to store the calculated RP in self (True) or discard them (False).

Returns

RP_i – Contraction of everything left of site i, with labels 'vL', 'vL*' for ket, bra.

Return type

Array

get_RP_age(i)[source]¶

Return number of physical sites in the contractions of get_RP(i).

Might be None.

get_initialization_data(first=0, last=None, include_bra=False, include_ket=False)[source]¶

Return data for (re-)initialization of the environment.

Parameters

first (int) – The first and last site, to the left and right of which we should return the environments. Defaults to 0 and L - 1.
last (int) – The first and last site, to the left and right of which we should return the environments. Defaults to 0 and L - 1.
include_bra (bool) – Whether to also return the bra and ket, respectively.
include_ket (bool) – Whether to also return the bra and ket, respectively.

Returns

init_env_data – A dictionary with the following entries.

init_LP, init_RPArray: LP on the left of site first and RP on the right of site last, which can be used as init_LP and init_RP for the initialization of a new environment.
age_LP, age_RPint: The number of physical sites involved into the contraction yielding init_LP and init_RP, respectively.
bra, ketMPS: References of bra and ket. Only included if include_bra and include_ket are True, respectively.

Return type

dict

get_op(op_list, i)[source]¶

Given a list of operators, select the one corresponding to site i.

Parameters

op_list ((list of) {str | npc.array}) – List of operators from which we choose. We assume that op_list[j] acts on site j. If the length is shorter than L, we repeat it periodically. Strings are translated using get_op() of site i.
i (int) – Index of the site on which the operator acts.

Returns

op – One of the entries in op_list, not copied.

Return type

npc.array

has_LP(i)[source]¶: Return True if LP left of site i is stored.

has_RP(i)[source]¶: Return True if RP right of site i is stored.

init_LP(i, start_env_sites=0)[source]¶

Build initial left part LP.

If bra and ket are the same and in left canonical form, this is the environment you get contracting he overlaps from the left infinity up to bond left of site i.

For segment MPS, the segment_boundaries are read out (if set).

Parameters

i (int) – Build LP left of site i.
start_env_sites (int) – How many sites to contract to converge the init_LP; the initial age_LP.

Returns

init_LP – Identity contractible with the vL leg of ket.get_B(i), labels 'vR*', 'vR'.

Return type

Array

init_RP(i, start_env_sites=0)[source]¶

Build initial right part RP for an MPS/MPOEnvironment.

If bra and ket are the same and in right canonical form, this is the environment you get contracting from the right infinity up to bond right of site i.

For segment MPS, the segment_boundaries are read out (if set).

Parameters

i (int) – Build RP right of site i.
start_env_sites (int) – How many sites to contract to converge the init_RP; the initial age_RP.

Returns

init_RP – Identity contractible with the vR leg of ket.get_B(i), labels 'vL*', 'vL'.

Return type

Array

init_first_LP_last_RP(init_LP=None, init_RP=None, age_LP=0, age_RP=0, start_env_sites=0)[source]¶

(Re)initialize first LP and last RP from the given data.

Parameters

init_LP (None | Array) – Initial very left part LP. If None, build one with :meth`init_LP`.
init_RP (None | Array) – Initial very right part RP. If None, build one with init_RP().
age_LP (int) – The number of physical sites involved into the contraction of init_LP.
age_RP (int) – The number of physical sites involved into the contraction of init_RP.
start_env_sites (int) – If init_LP and init_RP are not specified, contract each start_env_sites for them.

set_LP(i, LP, age)[source]¶: Store part to the left of site i.

set_RP(i, RP, age)[source]¶: Store part to the right of site i.

term_correlation_function_left(term_L, term_R, i_L=None, j_R=0, autoJW=True, opstr=None)[source]¶

Correlation function between (multi-site) terms, moving the left term, fix right term.

Same as term_correlation_function_right(), but vary index i of the left term instead of the j of the right term.

term_correlation_function_right(term_L, term_R, i_L=0, j_R=None, autoJW=True, opstr=None)[source]¶

Correlation function between (multi-site) terms, moving the right term, fix left term.

For term_L = [('A', 0), ('B', 1)] and term_R = [('C', 0), ('D', 1)], calculate the correlation function \(A_{i+0} B_{i+1} C_{j+0} D_{j+1}\) for fixed i and varying j according to i_L/j_R. The terms may not overlap. For fermions, the order of the terms is following the usual mathematical convention, where term_R acts first on a physical ket.

Warning

This function assumes that bra and ket are normalized, i.e. for MPSEnvironment. Thus you may want to take into account MPS.norm of both bra and ket.

Parameters

term_L (list of (str, int)) – Each a term representing a sum of operators on different sites, e.g., [('Sz', 0), ('Sz', 1)] or [('Cd', 0), ('C', 1)].
term_R (list of (str, int)) – Each a term representing a sum of operators on different sites, e.g., [('Sz', 0), ('Sz', 1)] or [('Cd', 0), ('C', 1)].
i_L (int) – Offset added to the indices of term_L.
j_R (list of int | None) – List of offsets to be added to the indices of term_R. Is sorted before use, i.e. the order is ignored. For finite MPS, None defaults to range(j0, L), where j0 is chosen such that term_R starts one site right of the term_L. For infinite MPS, None defaults to range(L, 11*L, L), i.e., one term per MPS unit cell for a distance of up to 10 unit cells.
autoJW (bool) – Whether to automatically take care of Jordan-Wigner strings.
opstr (str) – Force an intermediate operator string to used inbetween the terms. Can only be used in combination with autoJW=False.

Returns

corrs – Values of the correlation function, one for each entry in the list j_R.

Warning

The MPSEnvironment variant of this method takes the accumulated MPS norm into account, which is non-trivial e.g. when you used apply_local_op with non-unitary operators.

In contrast, the MPS variant of this method ignores the norm, i.e. returns the expectation value for the normalized state.

Return type

1D array

See also

correlation_function: varying both i and j at once.
term_list_correlation_function_right: generalization to sums of terms on the left/right.

term_list_correlation_function_right(term_list_L, term_list_R, i_L=0, j_R=None, autoJW=True, opstr=None)[source]¶

Correlation function between sums of multi-site terms, moving the right sum of term.

Generalization of term_correlation_function_right() to the case where term_list_L and term_R are sums of terms. This function calculates <bra|term_list_L[i_L] term_list_R[j]|ket> for j in j_R.

Assumes that overall terms with an odd number of operators requiring a Jordan-Wigner string don’t contribute. (In systems conserving the fermionic particle number (parity), this is true.)

Parameters

term_list_L (TermList) – Each a TermList representing the sum of terms to be applied.
term_list_R (TermList) – Each a TermList representing the sum of terms to be applied.
i_L (int) – Offset added to all the indices of term_list_L.
j_R (list of int | None) – List of offsets to be added to the indices of term_list_R. Is sorted before use, i.e. the order is ignored. For finite MPS, None defaults to range(j0, L), where j0 is chosen such that term_R starts one site right of the term_L. For infinite MPS, None defaults to range(L, 11*L, L), i.e., one term per MPS unit cell for a distance of up to 10 unit cells.
autoJW (bool) – Whether to automatically take care of Jordan-Wigner strings.
opstr (str) – Force an intermediate operator string to be used inbetween the terms. (Even used within the term_list_L/R for terms with smaller-than maximal support.) Can only be used in combination with autoJW=False.

Returns

corrs – Values of the correlation function, one for each entry in the list j_R.

Warning

The MPSEnvironment variant of this method takes the accumulated MPS norm into account, which is non-trivial e.g. when you used apply_local_op with non-unitary operators.

In contrast, the MPS variant of this method ignores the norm, i.e. returns the expectation value for the normalized state.

Return type

1D array

See also

term_correlation_function_right: version for a single term in both term_list_L/R.

test_sanity()[source]¶: Sanity check, raises ValueErrors, if something is wrong.