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

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We construct a short-range resonating valence-bond state (RVB) on the ruby lattice, using projected entangled-pair states (PEPS) with bond dimension D = 3. By introducing non-local moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining non-zero topological contribution, γ = −ln 2, consistent with that of a Z2 topological quantum spin liquid. We also calculate the ground-state energy of the spin-1 2 antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum-dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.

Section: A Projected Entangled-pair Statementioning

confidence: 99%

Section: Parent Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topological Z2 resonating-valence-bond quantum spin liquid on the ruby lattice

Jahromi

Orús

2020

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“…As the second benchmark, we use the gPEPS method to calculate the GS energy of the AFH model on the star lattice. The Hamiltonian of the AFH model on the star lattice reads [21]…”

Section: B Antiferromagnetic Heisenberg Model On 2d Star Latticementioning

confidence: 99%

Universal tensor-network algorithm for any infinite lattice

Jahromi

Orús

2019

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We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which codifies the details of tensor networks on any graphs in any dimension d, we are able to produce a code that can be essentially launched to simulate any lattice. We further introduce an optimized algorithm to compute simple tensor updates as well as expectation values and correlators with a mean-field-like effective environments. Though not being variational, this strategy allows to cope with PEPS of very large bond dimension (e.g., D = 100), and produces remarkably accurate results in the thermodynamic limit in many situations, and specially when the correlation length is small and the connectivity of the lattice is large. We prove the validity of our approach by benchmarking the algorithm against known results for several models, i.e., the antiferromagnetic Heisenberg model on a chain, star and cubic lattices, the hardcore Bose-Hubbard model on square lattice, the ferromagnetic Heisenberg model in a field on the pyrochlore lattice, as well as the 3-state quantum Potts model in field on the kagome lattice and the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice. We further demonstrate the performance of gPEPS by studying the quantum phase transition of the 2d quantum Ising model in transverse magnetic field on the square lattice, and the phase diagram of the Kitaev-Heisenberg model on the hyperhoneycomb lattice. Our results are in excellent agreement with previous studies. arXiv:1808.00680v3 [cond-mat.str-el]

“…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

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