Infinite-range Random Interactions Research Articles

Subsystem Rényi entropy of thermal ensembles for SYK-like models

The Sachdev-Ye-Kitaev model is an NN-modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large-NN limit. The results are consistent with exact diagonalization and can be well approximated by thermal entropy with an effective temperature when subsystem size M\leq N/2M≤N/2. We also consider generalizations of the SYK model with quadratic random hopping term or U(1)U(1) charge conservation.

Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model.

Quantum chaos is one of the distinctive features of the Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions in 0+1 dimensions with infinite-range two-body interactions, which is attracting a lot of interest as a toy model for holography. Here we show analytically and numerically that a generalized SYK model with an additional one-body infinite-range random interaction, which is a relevant perturbation in the infrared, is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature. However, a chaotic-integrable transition, characterized by the vanishing of the Lyapunov exponent and spectral correlations given by Poisson statistics, occurs at a temperature that depends on the strength of the perturbation. We speculate about the gravity dual of this transition.

Numerical study of fermion and boson models with infinite-range random interactions

We present numerical studies of fermion and boson models with random all-to-all interactions (the SYK models). The high temperature expansion and exact diagonalization of the $N$-site fermion model are used to compute the entropy density: our results are consistent with the numerical solution of $N=\infty$ saddle point equations, and the presence of a non-zero entropy density in the limit of vanishing temperature. The exact diagonalization results for the fermion Green's function also appear to converge well to the $N=\infty$ solution. For the hard-core boson model, the exact diagonalization study indicates spin glass order. Some results on the entanglement entropy and the out-of-time-order correlators are also presented.

First-order quantum phase transition in an anisotropic Ising model with infinite-range random interaction

First-order quantum phase transition in an anisotropic Ising model with infinite-range random interaction

One-step replica symmetry breaking solution of the quadrupolar glass model

We consider the quadrupolar glass model with infinite-range random interaction. Introducing a simple one-step replica symmetry breaking ansatz we investigate the para-glass continuous (discontinuous) transition which occurs below (above) a critical value of the quadrupole dimension m*. By using a mean-field approximation we study the stability of the one-step replica symmetry breaking solution and show that for m>m* there are two transitions. The thermodynamic transition is discontinuous but there is no latent heat. At a higher temperature we find the dynamical or glass transition temperature and the corresponding discontinuous jump of the order parameter.

Equilibrium properties of a quadrupolar glass.

We introduce a semimicroscopic discrete-state model appropriate to the orientational glass phase in mixed alkali halide cyanides with 〈111〉 equilibrium orientations of the ${\mathrm{CN}}^{\mathrm{\ensuremath{-}}}$ ions, such as K(CN${)}_{\mathit{x}}$${\mathrm{Br}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$. The order-parameter fields are defined as symmetry adapted combinations of the occupation number operators along the cubic body diagonals, which transform according to the ${\mathit{T}}_{2\mathit{g}}$ representation of the cubic group. These interact via an infinite-range random interaction in the presence of quenched local random strains. We then use the replica formalism to derive a replica-symmetric solution for the components of the orientational-glass order parameter, the linear susceptibilities, and the elastic compliances. The high-temperature orientational-glass phase is characterized by an isotropic order-parameter matrix with only the diagonal elements ${\mathit{q}}_{\mathrm{\ensuremath{\mu}}}$ being nonzero. At high temperatures, the behavior of the order parameter q=${\mathrm{\ensuremath{\Sigma}}}_{\mathrm{\ensuremath{\mu}}}$${\mathit{q}}_{\mathrm{\ensuremath{\mu}}}$/3 is similar to that of an Ising spin glass, however, at intermediate and low temperatures the two models differ significantly. We also derive the instability line ${\mathit{T}}_{\mathit{f}}$(\ensuremath{\Delta}) separating the replica-symmetric isotropic phase from the low-temperature anisotropic orientational glass phase, which is characterized by broken replica symmetry. In contrast to the random-bond--random-field model of an Ising spin glass, the instability temperature increases with random-field variance, implying that in quadrupolar glasses replica-symmetry breaking may be relevant already at relatively high temperatures. Finally, an expression for the distribution of local strains related to the NMR line shape is derived. It is also shown that the quadrupolar glass order parameter can be determined by NMR.

Monte Carlo simulation of a quasi one-dimensional spin glass

A recently introduced model of a quasi one-dimensional spin glass by means of Monte Carlo simulations was studied. The model consists of linear chains of Ising spins with ferromagnetic nearest-neighbour interchain coupling of strength, K, in addition to infinite-range random interactions. The Edwards-Anderson order parameter and the field-cooled and zero-field-cooled susceptibilities are evaluated for various values of K.

Superconducting glass behaviour in the random interaction Hubbard model

The extended Hubbard model with on-site attraction and random infinite-range inter-site Coulomb interaction is studied for the arbitrary band filling. In the strong coupling regime the problem is mapped onto a system of hard-core bosons (local electron pairs) on a lattice described by the anisotropic pseudo-spin model with infinite-range random interactions — in close analogy to the standard Sherrington-Kirkpatrick spin-glass approach. The stability of the mean-field-type solution against the action of fluctuation is investigated in the parameter space including: the temperature, degree of disorder and band filling parameter.

Spherical spin-glass models with short-range ferromagnetic interaction: Thermodynamics and correlation functions.

The free energy is solved for spherical spin-glass models with nearest-neighbor ferromagnetic and infinite-range random interactions, of either random-bond or random-site type. The long-range random-bond interaction destroys the ferromagnetic phase for 2<d\ensuremath{\le}4, whereas the random-site interaction does not. The spin-glass--ferromagnetic phase-transition scaling laws, satisfied in the random-site model, are not valid in the random-bond model. Correlation functions of the order parameters are evaluated.

Solvable model of a quadrupolar glass

A quadrupolar model with infinite-range random interaction is considered in the frame of a replica-symmetric approach. The equations for orientational and glass order parameters have no trivial solution and do not indicate phase transitions. The orientationally ordered and glass regimes grow continuously on cooling. The entropy at T=0 is positive.

Comment on the critical dynamics of the SK model

It is pointed out that recent work on the critical dynamics of the Sherrington-Kirkpatrick (SK) model (1975) contains some important errors, and the correct value Delta m=1 is derived for the critical index of the uniform magnetisation. It is concluded that the SK model is equivalent to the spherical model with infinite-range random interactions in respect of the critical behaviour.