Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice

Haghshenas, Reza; Gong, Shou-Shu

doi:10.1103/physrevb.99.174423

Cited by 19 publications

(7 citation statements)

References 66 publications

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“…Numerical studies of H at B Z = 0 and J χ = 0 on the kagome [11][12][13] and triangular [14][15][16][17] lattices have found convincing evidence, above very small values of J χ (values as small as J χ /J 1 = 0.0014 in Fig. 19 of Ref.…”

Section: At Low Temperatures (T )mentioning

confidence: 90%

Enhanced thermal Hall effect in the square-lattice Néel state

et al. 2019

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Recent experiments on several cuprate compounds have identified an enhanced thermal Hall response in the pseudogap phase. Most strikingly, this enhancement persists even in the undoped system, which challenges our understanding of the insulating parent compounds. To explain these surprising observations, we study the quantum phase transition of a squarelattice antiferromagnet from a confining Néel state to a state with coexisting Néel and semion topological order. The transition is driven by an applied magnetic field and involves no change in the symmetry of the state. The critical point is described by a strongly-coupled conformal field theory with an emergent global SO(3) symmetry. The field theory has four different formulations in terms of SU (2) or U (1) gauge theories, which are all related by dualities; we relate all four theories to the lattice degrees of freedom. We show how proximity of the confining Néel state to the critical point can explain the enhanced thermal Hall effect seen in experiment.

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Section: At Low Temperatures (T )mentioning

confidence: 90%

Enhanced thermal Hall effect in the square-lattice Néel state

et al. 2019

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“…Therefore, we have to use an alternative way to perform the local update process by direct minimizing the error function [47,49],…”

Section: Methodsmentioning

confidence: 99%

Simulation of the Ring-exchange Models with Projected Entangled Pair States

Wang,

Dong,

Han

et al. 2021

Preprint

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Algorithms to simulate the ring-exchange models using the projected entangled pair states (PEPS) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange interactions. We compare the effects of different approximations to the environment. To understand the numerical instability during the optimization, we introduce the "singularity" of a PEPS and develop a regulation procedure that can effectively reduce the singularity of a PEPS. We benchmark our method with the toric code model, and obtain extremely accurate ground state energies and topological entanglement entropy. We also benchmark our method with the two-dimensional cyclic ring exchange model, and find that the ground state has a strong vector chiral order. The algorithms can be a powerful tool to investigate the models with ring interactions. The methods developed in this work, e.g., the regularization process to reduce the singularity can also be applied to other models.

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“…Numerical studies of H spin on the square [39] and other lattices [40][41][42][43][44][45][46] have found evidence of a chiral spin liquid…”

Section: Spin Liquid Ansatz On the Square Latticementioning

confidence: 99%

Phonon Hall viscosity from phonon-spinon interactions

et al. 2021

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Motivated by experimental observations, Samajdar et al. [Nature Physics 15, 1290] have proposed that the insulating Néel state in the parent compounds of the cuprates is proximate to a quantum phase transition to a state in which Néel order coexists with semion topological order. We study the manner in which proximity to this transition can make the phonons chiral, by inducing a significant phonon Hall viscosity. We describe the spinon-phonon coupling in a lattice spinon model coupled to a strain field, and also using a general continuum theory constrained only by symmetry. We find a nonanalytic Hall viscosity across the transition, with a divergent second derivative at zero temperature.

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Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice

Cited by 19 publications

References 66 publications

Enhanced thermal Hall effect in the square-lattice Néel state

Enhanced thermal Hall effect in the square-lattice Néel state

Simulation of the Ring-exchange Models with Projected Entangled Pair States

Phonon Hall viscosity from phonon-spinon interactions

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