Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction

Dai, Yan-Wei; Shi, Qian-Qian; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan‐Qiang

doi:10.1103/physrevb.95.214409

Cited by 25 publications

(14 citation statements)

References 62 publications

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“…While the rank of the tensors used in the representation is determined by the physical problem, the amount of information they contain is determined by their bond dimension, D, which is used to control the accuracy of the ansatz. Although iPEPS were introduced originally for representing the ground states of local Hamiltonians, more recently several iPEPS methods have been developed for the representation of thermal states [36,[52][53][54][55][56][57][58][59][60][61][62]. Here we focus on the approaches discussed in Ref.…”

Section: Thermodynamics From Ipepsmentioning

confidence: 99%

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

Wietek

Corboz

Weßel

et al. 2019

Phys. Rev. Research

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The thermodynamic properties of the Shastry-Sutherland model have posed one of the longestlasting conundrums in frustrated quantum magnetism. Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product to the plaquette-based ground state, neither analytical nor any available numerical methods have come close to reproducing the physics of the excited states and thermal response. We solve this problem in the dimer-product phase by introducing two qualitative advances in computational physics. One is the use of thermal pure quantum (TPQ) states to augment dramatically the size of clusters amenable to exact diagonalization. The second is the use of tensor-network methods, in the form of infinite projected entangled pair states (iPEPS), for the calculation of finite-temperature quantities. We demonstrate convergence as a function of system size in TPQ calculations and of bond dimension in our iPEPS results, with complete mutual agreement even extremely close to the QPT. Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat around the QPT, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states. The surprisingly low energy scale and apparently extended spatial nature of these states explain the failure of less refined numerical approaches to capture their physics. Both of our methods will have broad and immediate application in addressing the thermodynamic response of a wide range of highly frustrated magnetic models and materials.

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Section: Thermodynamics From Ipepsmentioning

confidence: 99%

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

Wietek

Corboz

Weßel

et al. 2019

Phys. Rev. Research

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“…Its power was demonstrated, e.g., by a solution of the longstanding magnetization plateaus problem in the highly frustrated compound SrCu 2 (BO 3 ) 2 34,35 , establishing the striped nature of the ground state of the doped 2D Hubbard model 36 , and new evidence supporting gapless spin liquid in the kagome Heisenberg antiferromagnet 37 . Recent developments in iPEPS optimization [38][39][40] , contraction 41,42 , energy extrapolations 43 , and universalityclass estimation [44][45][46] pave the way towards even more complicated problems, including simulation of thermal states [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63] , mixed states of open systems 55,64,65 , excited states 66,67 , or real-time evolution 55,[68][69][70][71][72][73][74][75] . In parallel with iPEPS, there is continuous progress in simulating systems on cylinders of finite width using DMRG.…”

Section: Introductionmentioning

confidence: 99%

Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update

Dziarmaga

2021

Preprint

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“…[9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Besides the computation of ground states, for which (i)PEPS was originally developed, significant progress has also been achieved in other applications, including the study of thermodynamic properties [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42], excited states [43,44], real-time evolution [36,[45][46][47] and open systems [36,48]. * p.c.g.vlaar@uva.nl…”

Section: Introductionmentioning

confidence: 99%

Simulation of three-dimensional quantum systems with projected entangled-pair states

Vlaar,

Corboz

2021

Preprint

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Tensor network algorithms have proven to be very powerful tools for studying one-and twodimensional quantum many-body systems. However, their application to three-dimensional (3D) quantum systems has so far been limited, mostly because the efficient contraction of a 3D tensor network is very challenging. In this paper we develop and benchmark two contraction approaches for infinite projected entangled-pair states (iPEPS) in 3D. The first approach is based on a contraction of a finite cluster of tensors including an effective environment to approximate the full 3D network. The second approach performs a full contraction of the network by first iteratively contracting layers of the network with a boundary iPEPS, followed by a contraction of the resulting quasi-2D network using the corner transfer matrix renormalization group. Benchmark data for the Heisenberg and Bose-Hubbard models on the cubic lattice show that the algorithms provide competitive results compared to other approaches, making iPEPS a promising tool to study challenging open problems in 3D.

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Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction

Cited by 25 publications

References 62 publications

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update

Simulation of three-dimensional quantum systems with projected entangled-pair states

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