Residual entropies for three-dimensional frustrated spin systems with tensor networks

Vanderstraeten, Laurens; Vanhecke, Bram; Verstraete, Frank

doi:10.1103/physreve.98.042145

Cited by 56 publications

(58 citation statements)

References 31 publications

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“…These results agree well with the other results in [51,52], which were estimated by other simulation methods. The temperature dependence of average helix length of deca-alanine.…”

Section: Appendix B: Applications Of Rewl-mucaremsupporting

confidence: 92%

Efficient simulation protocol for determining the density of states: Combination of replica-exchange Wang-Landau method and multicanonical replica-exchange method

Hayashi

Okamoto

2019

Phys. Rev. E

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By combining two generalized-ensemble algorithms, Replica-Exchange Wang-Landau (REWL) method and Multicanonical Replica-Exchange Method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed next. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model by the three methods, namely, REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by the REWL-MUCAREM is more accurate than that is estimated by the two methods separately.

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“…These results agree well with the other results in [51,52], which were estimated by other simulation methods. The temperature dependence of average helix length of deca-alanine.…”

Section: Appendix B: Applications Of Rewl-mucaremsupporting

confidence: 92%

Efficient simulation protocol for determining the density of states: Combination of replica-exchange Wang-Landau method and multicanonical replica-exchange method

Hayashi

Okamoto

2019

Phys. Rev. E

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show abstract

“…4, where we focus on the part of the TM spectrum corresponding to U (1) charge u = 1 with the refinement parameter δ defined in this sector according to Eq. (14). We present the splitting of the dominant part of the TM spectrum for a single D in the inset of panel (a).…”

Section: Distance From Exact Solution δmentioning

confidence: 99%

“…Panel (a) shows extrapolation of the correlation length for selected values of ∆. Refinement parameter δ is calculated from sector with U(1) charge u = 1, Eq (14)…”

mentioning

confidence: 99%

Precise Extrapolation of the Correlation Function Asymptotics in Uniform Tensor Network States with Application to the Bose-Hubbard and XXZ Models

2018

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We analyze the problem of extracting the correlation length from infinite matrix product states (MPS) and corner transfer matrix (CTM) simulations. When the correlation length is calculated directly from the transfer matrix, it is typically significantly underestimated for finite bond dimensions used in numerical simulation. This is true even when one considers ground states at a distance from the critical point. In this article we introduce extrapolation procedure to overcome this problem. To that end we quantify how much the dominant part of the MPS/CTM transfer matrix spectrum deviates from being continuous. The latter is necessary to capture the exact asymptotics of the correlation function where the exponential decay is typically modified by an additional algebraic term. By extrapolating such a refinement parameter to zero, we show that we are able to recover the exact value of the correlation length with high accuracy. In a generic setting, our method reduces the error by a factor of ∼ 100 as compared to the results obtained without extrapolation and a factor of ∼ 10 as compared to simple extrapolation schemes employing bond dimension. We test our approach in a number of solvable models both in 1d and 2d. Subsequently, we apply it to one-dimensional XXZ spin-3 2 and the Bose-Hubbard models in a massive regime in the vicinity of the Berezinskii-Kosterlitz-Thouless critical point. We then fit the scaling form of the correlation length and extract the position of the critical point and obtain results comparable or better than those of other state-of-the-art numerical methods. Finally, we show how the algebraic part of the correlation function asymptotics can be directly recovered from the scaling of the dominant form factor within our approach. Our method provides the means for detailed studies of phase diagrams of quantum models in 1d and, through the finite correlation length scaling of projected entangled pair states, also in 2d.

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“…30. Using recently developed contraction methods for three-dimensional tensor networks 40 , we stress that such an approach can also be applied in threedimensional systems, as recently illustrated in Ref. 41. where |0 = ⊗ l |0 l , and N is a normalization factor.…”

Section: Discussionmentioning

confidence: 85%

Tensor-network approach to phase transitions in string-net models

et al. 2019

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We use a recently proposed class of tensor-network states to study phase transitions in stringnet models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops expectation values, and a natural order parameter detecting the breakdown of the topological phase. In the presence of a string tension, a quantum phase transition occurs between the topological phase and a trivial phase. We benchmark our approach for Z2 string nets and capture the second-order phase transition which is well known from the exact mapping onto the transverse-field Ising model. More interestingly, for Fibonacci string nets, we obtain first-order transitions in contrast with previous studies but in qualitative agreement with mean-field results.

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Residual entropies for three-dimensional frustrated spin systems with tensor networks

Cited by 56 publications

References 31 publications

Efficient simulation protocol for determining the density of states: Combination of replica-exchange Wang-Landau method and multicanonical replica-exchange method

Efficient simulation protocol for determining the density of states: Combination of replica-exchange Wang-Landau method and multicanonical replica-exchange method

Precise Extrapolation of the Correlation Function Asymptotics in Uniform Tensor Network States with Application to the Bose-Hubbard and XXZ Models

Tensor-network approach to phase transitions in string-net models

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