Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

Iregui, Juan Osorio; Corboz, Philippe; Troyer, Matthias

doi:10.1103/physrevb.90.195102

Cited by 54 publications

(37 citation statements)

References 43 publications

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“…1-(d)). Next, by associating an iPEPS tensor to each block site and introducing trivial indices [22] as in the yellow dotted lines in Fig. 1-(d), we end up with an iPEPS on the square lattice and a 2 × 2 unit cell specified by two tensors A and B according to a checkerboard pattern, see Fig.…”

Section: B Ruby Lattice and Trotterizationmentioning

confidence: 99%

“…However, the downside is that the CTM method is only applied straightforwardly to the 2D square lattice, whereas for other lattice structures this may not be obvious at all. In any case, the method has also been successfully applied to other cases such as the honeycomb [22] and kagome [14,23,24] lattices. In spite of the success of current TN algorithms for the study of quantum many-body systems, there are still many interesting models, which are left behind due to their complicated interactions and lattice structures, thus making the implementation challenging.…”

Section: Introductionmentioning

confidence: 99%

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Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

et al. 2018

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The infinite Projected Entangled-Pair State (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearestneighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the Corner Transfer Matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the groundstate properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground state fidelity and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.arXiv:1711.04798v2 [cond-mat.str-el]

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Section: B Ruby Lattice and Trotterizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

et al. 2018

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“…The only essential parameter which controls the accuracy of the ansatz is the so-called bond dimension D. In order to obtain highly accurate results, one should use a novel optimization scheme to access large bond dimension and to perform reliable bond-dimension scaling. iPEPS has been shown successful to study challenging problems of interacting fermions (including t-J and Hubbard models) [41][42][43] and frus-trated spin systems [44][45][46][47][48][49] . Besides model simulation, PEPS can also be constructed to strictly describe novel quantum states.…”

Section: Introductionmentioning

confidence: 99%

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

Haghshenas

Gong

2019

Phys. Rev. B

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We study the antiferromagnetic kagome Heisenberg model with additional scalar-chiral interaction by using the infinite projected entangled-pair state (iPEPS) ansatz. We discuss in detail the implementation of optimization algorithm in the framework of the single-layer tensor network based on the corner-transfer matrix technique. Our benchmark based on the full-update algorithm shows that the single-layer algorithm is stable, which leads to the same level of accuracy as the double-layer ansatz but with much less computation time. We further apply this algorithm to study the nature of the kagome Heisenberg model with a scalar-chiral interaction by computing the bond dimension scaling of magnetization, bond energy difference, chiral order parameter and correlation length. In particular, we find that for strong chiral coupling the correlation length, which is extracted from the transfer matrix, saturates to a finite value for large bond dimension, representing a gapped spin-liquid state. Further comparison with density matrix renormalization group results supports that our iPEPS faithfully represents the time-reversal symmetry breaking chiral state. Our iPEPS simulation results shed new light on constructing PEPS for describing gapped chiral topological states. PACS numbers: 75.40.Mg, 75.10.Jm, 75.10.Kt, 02.70.-c arXiv:1812.11436v3 [cond-mat.str-el] 23 May 2019 J ch EiPEPS m ∆Tx−y Hc J ch = 0.5 −0.4768 0.004 0.004 0.172 J ch = 2.0 −0.6889 0.006 0.002 0.231 J ch = ∞ −0.1715 0.009 0.0005 0.254

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“…[18][19][20] In this respect, the Kitaev honeycomb model has been a prominent candidate. [21][22][23][24][25][26] The Hamiltonian of this model contains two-body interactions (hence relatively easier to realize experimentally), and has a rich phase diagram that exhibits different classes of topological phases and non-Abelian anyons. In addition, the Kitaev honeycomb model on an arbitrary-row brick-wall lattice (another representation of the honeycomb lattice) has also been recently studied.…”

Section: Introductionmentioning

confidence: 99%

Characterization of topological phases in the compass ladder model

Haghshenas

Langari

Rezakhani

2016

J. Phys.: Condens. Matter

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We characterize phases of the compass ladder model by using degenerate perturbation theory, symmetry fractionalization, and numerical techniques. Through degenerate perturbation theory we obtain an effective Hamiltonian for each phase of the model, and show that a cluster model and the Ising model encapsulate the nature of all phases. In particular, the cluster phase has a symmetry-protected topological order, protected by a specific Z2 ×Z2 symmetry, and the Ising phase has a Z2-symmetry-breaking order characterized by a local order parameter expressed by the magnetization exponent 0.12 ± 0.01. The symmetry-protected topological phases inherit all properties of the cluster phases, although we show analytically and numerically that they belong to different classes. In addition, we study the one-dimensional quantum compass model, which naturally emerges from the compass ladder, and show that a partial symmetry breaking occurs upon quantum phase transition. We numerically demonstrate that a local order parameter accurately determines the quantum critical point and its corresponding universality class.

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Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

Cited by 54 publications

References 43 publications

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

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

Characterization of topological phases in the compass ladder model

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