Geometry dependence of the sign problem in quantum Monte Carlo simulations

Iglovikov, Vladimir; Khatami, Ehsan; Scalettar, Richard

doi:10.1103/physrevb.92.045110

Cited by 94 publications

(76 citation statements)

References 62 publications

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“…Such results are difficult to obtain, as computational methods formulated on finite lattices (such as ED, DMRG, and cluster DMFT) pro-vide limited momentum resolution. In addition, quantum Monte Carlo approaches are impeded by a sign problem in frustrated systems [34]. Results for these quantities are therefore often obtained from fits to quantum spin models, which are only justified in the large Coulomb interaction limit.…”

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confidence: 99%

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Gull

2020

Phys. Rev. Research

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We study magnetic and charge susceptibilities in the half-filled two-dimensional triangular Hubbard model within the dual fermion approximation in the metallic, Mott insulating, and crossover regions of parameter space. In the insulating state, we find strong spin fluctuations at the K point at low energy corresponding to the 120 • antiferromagnetic order. These spin fluctuations persist into the metallic phase and move to higher energy. We also present data for simulated neutron spectroscopy and spin-lattice relaxation times, and perform direct comparisons to inelastic neutron spectroscopy experiments on the triangular material Ba8CoNb6O24 and to the relaxation times on κ-(ET)2Cu2(CN)3. Finally, we present charge susceptibilities in different areas of parameter space, which should correspond to momentum-resolved electron-loss spectroscopy measurements on triangular compounds., suggests that these compounds are close to a two-dimensional triangular structure and exhibit interesting electron correlation behavior including, potentially, a quantum spin liquid phase [7] in the ground state [8]. These compounds, as well as the low energy physics of the fully isotropic triangular material Ba 8 CoNb 6 O 24 [9], may be described by a half-filled single orbital Hubbard model on a triangular two-dimensional lattice, with an on-site Coulomb interaction strength comparable to or larger than the bandwidth [10].Because of the subtle competition of metallic, ordered, and spin liquid phases in the ground state, this model has been studied extensively with a wide range of numerical tools, including exact diagonalization (ED) [11][12][13], density matrix renormalization group theory (DMRG) [8], variational Monte Carlo (VMC) [14][15][16][17], variational cluster approximation [18][19][20], strong coupling expansions [21], path integral renormalization group techniques [22], and cluster dynamical mean field theory (DMFT) in the cellular [23][24][25][26][27] and dynamical cluster [28,29] variants. The focus in most of these studies has been on the precise location of the phase boundaries, ordering (or the absence thereof), and on the nature of these phases.Experimentally, much of our knowledge about correlated triangular systems is obtained from single-and two-particle scattering experiments such as photoemission [30], Raman spectroscopy [31], nuclear magnetic resonance (NMR) [2,32], or inelastic neutron scattering [9,33]. To understand these experimental results, it is necessary to calculate the corresponding response functions as a function of energy and momentum. For neutron spectroscopy and angular-resolved photoemission spectroscopy, in particular, both fine momentum and energy resolutions are desired. Such results are difficult to obtain, as computational methods formulated on finite lattices (such as ED, DMRG, and cluster DMFT) pro-

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confidence: 99%

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Gull

2020

Phys. Rev. Research

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“…Work aimed at recognizing where and when a sign problem does not exist, is not new, but few systematic approaches to this problem exist. Most of the work has been focused on understanding the sign problem for specific classes of Hamiltonians of physical interest, for example Fermi-Hubbard models [15]. An example of a recent exploration relating stoquasticity to timereversal for fermionic systems is [16] (see [17] for a recent review).…”

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Two-local qubit Hamiltonians: when are they stoquastic?

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Terhal

2019

Quantum

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We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for n-qubit Hamiltonians with identical 2local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary n-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes.Accepted in Quantum 2019-03-29, click title to verify arXiv:1806.05405v3 [quant-ph] 29 Apr 2019 1 It is worthwhile noting that the entrywise non-negativity of the matrix exp(−H/kT ) for a given temperature T does not imply that H is a symmetric Z-matrix. It is simple to generate numerical 4 × 4 cases where G = A T A is a non-negative matrix by taking A as a non-negative matrix, but H = − log G is not a symmetric Z-matrix. Thus when H is a symmetric Z-matrix, the non-negativity of exp(−H/kT ) is guaranteed for all values of kT , while in other cases exp(−H/kT ) might be non-negative only for sufficiently small values of kT .2 [1] points out that for 2-local Hamiltonians one can prove that termwise stoquastic is the same as stoquastic. This is however not true for k > 2-local Hamiltonians generally.

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“…Our computational method, determinant quantum Monte Carlo (QMC) calculations [18,19], treats disorders and interactions on an equal, exact footing, and provides a solution to the Hubbard Hamiltonian on lattices of finite spatial size, when the sign problem is not too serious [20][21][22][23][24]. We focus on the disorder dependence of the entropy SðTÞ, obtained via a thermodynamic integration of the energy [25] down from T ¼ ∞.…”

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Cooling Atomic Gases With Disorder

et al. 2015

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Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing, and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a nondisordered state which exhibits these incompletely understood phases. We show, using quantum Monte Carlo simulations, that we can approach the Néel temperature of the threedimensional Hubbard model for experimentally achievable parameters. Recent experimental estimates suggest the randomness required lies in a regime where atom transport and equilibration are still robust. [5,6]. Ultracold atomic gases offer the opportunity to emulate these fundamental issues using optical speckle [7,8], impurities [9], or a quasiperiodic optical lattice [10,11] to introduce randomness. In the bosonic case, the competition between strong interactions and strong disorder has been studied in the context of the elusive Bose glass phase [7,9,11], while for fermions, a recent experiment has explored disorder-induced localization in the three-dimensional (3D) Hubbard model of strongly interacting fermions [12].In this paper, we explore the thermodynamics of interacting, disordered systems and suggest that, in addition to studies of the many-body phenomena noted above, preparing a gas in a random potential might be exploited to cool the atoms. Specifically, we show using an unbiased numerical method that one can lower the temperature and access the regime with long-range magnetic order by adiabatically decreasing the randomness in the chemical potential or hopping energies of the Hubbard Hamiltonian. The achievement of new quantum phases in cold atom experiments largely depends on the reduction of the entropy per particle. The success of our proposal requires that the gas would have to be cooled (e.g. evaporatively) after the disorder is in place. We will return in the

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Geometry dependence of the sign problem in quantum Monte Carlo simulations

Cited by 94 publications

References 62 publications

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Two-local qubit Hamiltonians: when are they stoquastic?

Cooling Atomic Gases With Disorder

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