Variational wave functions for Sachdev-Ye-Kitaev models

Haldar, Arijit; Tavakol, Omid; Scaffidi, Thomas

doi:10.1103/physrevresearch.3.023020

Cited by 10 publications

(6 citation statements)

References 54 publications

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“…Reference [76] also considers two SYK clusters and quartic couplings between them, but the sizes of the two clusters are parametrically different, so that one acts as a bath for the other. Several other two-flavor or two-species SYK variants have also appeared in the literature [77][78][79][80].…”

Section: Discussion and Contextmentioning

confidence: 98%

Bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics

2022

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We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-N in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite-size spectral properties of the model. We show how the level statistics differs from the original SYK model and infer an additional exchange symmetry in the bipartite model.

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Section: Discussion and Contextmentioning

confidence: 98%

Bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics

2022

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“…Then, using standard random matrix bounds on the operator norm of the matrix with independent entries and a triangle inequality gives us the desired bound on J mat op. We use similar bounds elsewhere and [HTS21] uses the same bound.…”

Section: Degree-6 Sum-of-squares For Sykmentioning

confidence: 99%

“…To evaluate tr(ghg * ), we give a representation in terms of matrices (essentially the same representation is used in [HTS21]). Define a matrix m whose rows and columns are indexed by subsets of [n] with cardinality q 2.…”

Section: Fooling Degree Qmentioning

confidence: 99%

“…The requirement (ii) is necessary as otherwise one could simply declare that the state is exp(βp) φ⟩ for large β > 0 and for φ chosen to have nontrivial projection on the eigenspace of maximal eigenvalue; as β → ∞, this state converges to that eigenspace, but we cannot compute expectation values efficiently. Another interesting state that does not seem to meet our requirements is the coupled cluster variational state of[HTS21].…”

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confidence: 97%

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Optimizing Strongly Interacting Fermionic Hamiltonians

Hastings¹,

O’Donnell²

2021

Preprint

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The fundamental problem in much of physics and quantum chemistry is to optimize a lowdegree polynomial in certain anticommuting variables. Being a quantum mechanical problem, in many cases we do not know an efficient classical witness to the optimum, or even to an approximation of the optimum. One prominent exception is when the optimum is described by a so-called "Gaussian state", also called a free fermion state. In this work we are interested in the complexity of this optimization problem when no good Gaussian state exists. Our primary testbed is the Sachdev-Ye-Kitaev (SYK) model of random degree-q polynomials, a model of great current interest in condensed matter physics and string theory, and one which has remarkable properties from a computational complexity standpoint. Among other results, we give an efficient classical certification algorithm for upper-bounding the largest eigenvalue in the q = 4 SYK model, and an efficient quantum certification algorithm for lower-bounding this largest eigenvalue; both algorithms achieve constant-factor approximations with high probability.

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“…-We begin by discussing the nematic order which appears as a symmetry breaking solution to the above equations with Σ + = Σ − . This phase may be viewed as a lattice generalization of the flavorimbalanced phase of a two-flavor SYK model [52,68]. As shown in Fig.…”

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confidence: 99%

Nematic phases and elastoresistivity from a multiorbital strange metal

Hardy¹,

Haldar²,

Paramekanti³

2022

Preprint

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We propose and study a two-orbital lattice extension of the Sachdev-Ye-Kitaev model in the large-N limit. The phase diagram of this model features a high temperature isotropic strange metal which undergoes a first-order thermal transition into a nematic insulator or a continuous thermal transition into nematic metal phase, separated by a tunable tricritical point. These phases arise from spontaneous partial orbital polarization of the multiorbital non-Fermi liquid. We explore the spectral and transport properties of this model, including the d.c. elastoresistivity, which exhibits a peak near the nematic transition, as well as the nonzero frequency elastoconductivity. Our work offers a useful perspective on nematic phases and transport in correlated multiorbital systems.

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Variational wave functions for Sachdev-Ye-Kitaev models

Cited by 10 publications

References 54 publications

Bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics

Bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics

Optimizing Strongly Interacting Fermionic Hamiltonians

Nematic phases and elastoresistivity from a multiorbital strange metal

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