Tensor network simulation of the Kitaev-Heisenberg model at finite temperature

Czarnik, Piotr; Francuz, Anna; Dziarmaga, Jacek

doi:10.1103/physrevb.100.165147

Cited by 26 publications

(16 citation statements)

References 95 publications

(125 reference statements)

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“…Our techniques have the added value of directly tackling the thermodynamic limit: Residual finite-size effects are encompassed by the so-called bond dimension of the ansatz and could be accounted for in a rather systematic way [40][41][42][43][44]. These features have made two-dimensional tensor networks a very suitable tool for studying intricate condensed matter problems, not only via their ground states [45][46][47][48] but even beyond [49][50][51][52][53][54], as well as finite temperature properties of both classical and quantum models in two spatial dimensions [33,34,[55][56][57][58][59][60][61][62]. The present work builds upon and develops this substantial technical machinery.…”

Section: Introductionmentioning

confidence: 99%

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

et al. 2021

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The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the O(3)O(3) non-linear sigma model in 1+11+1 dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in 3+13+1 dimensions), namely the phenomenon of asymptotic freedom. This should also exclude finite-temperature transitions, but lattice effects might play a significant role in correcting the mainstream picture. In this work, we make use of state-of-the-art tensor network approaches, representing the classical partition function in the thermodynamic limit over a large range of temperatures, to comprehensively explore the correlation structure for Gibbs states. By implementing an SU(2)SU(2) symmetry in our two-dimensional tensor network contraction scheme, we are able to handle very large effective bond dimensions of the environment up to \chi_E^\text{eff} \sim 1500χEeff∼1500, a feature that is crucial in detecting phase transitions. With decreasing temperatures, we find a rapidly diverging correlation length, whose behaviour is apparently compatible with the two main contradictory hypotheses known in the literature, namely a finite-TT transition and asymptotic freedom, though with a slight preference for the second.

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Section: Introductionmentioning

confidence: 99%

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

et al. 2021

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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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“…Heisenberg) interactions and external magnetic fields, all of which spoil the Kitaev model's exact solvability and often favor magnetically ordered ground states. One therefore must resort to numerical methods [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], such as exact diagonalization (ED), tensor-network techniques like the density-matrix renormalization group (DMRG) [51][52][53], and Monte Carlo [54,55], to study the ground-state phase diagram. Thus, Kitaev models provide a useful benchmark for near-term quantum algorithms for the study of interacting quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model

Li,

Alam,

Iadecola

et al. 2021

Preprint

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Quantum spin systems may offer the first opportunities for beyond-classical quantum computations of scientific interest. While general quantum simulation algorithms likely require errorcorrected qubits, there may be applications of scientific interest prior to the practical implementation of quantum error correction. The variational quantum eigensolver (VQE) is a promising approach to find energy eigenvalues on noisy quantum computers. Lattice models are of broad interest for use on near-term quantum hardware due to the sparsity of the number of Hamiltonian terms and the possibility of matching the lattice geometry to the hardware geometry. Here, we consider the Kitaev spin model on a hardware-native square-octagon qubit connectivity map, and examine the possibility of efficiently probing its rich phase diagram with VQE approaches. By benchmarking different choices of variational ansatz states and classical optimizers, we illustrate the advantage of a mixed optimization approach using the Hamiltonian variational ansatz (HVA). We further demonstrate the implementation of an HVA circuit on Rigetti's Aspen-9 chip with error mitigation.

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Tensor network simulation of the Kitaev-Heisenberg model at finite temperature

Cited by 26 publications

References 95 publications

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

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

Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model

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