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We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state,…
We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems with strong correlations (at and near a critical point). In our approach, we derive a…
For a parameterized family of invertible states (short-range-entangled states) in $(1+1)$ dimensions, we discuss a generalization of the Berry phase. Using translationally-invariant, infinite matrix product states (MPSs), we introduce a…
We investigate the dressed bound states (DBS) in an open cavity with a whispering-gallery-mode microring coupled to a two-level atom and a waveguide with a mirror at the right end. We demonstrate that the non-Hermiticity of an open cavity…
Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product Ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of…
We consider the open XYZ spin chain with boundary fields. We solve the model by the new Separation of Variables approach introduced in arXiv:1904.00852. In this framework, the transfer matrix eigenstates are obtained as a particular…
Interacting systems with $K$ driven particle species on a open chain or chains which are coupled at the ends to boundary reservoirs with fixed particle densities are considered. We classify discontinuous and continuous phase transitions…
Complex free-energy landscapes with many local minima separated by large barriers are believed to underlie glassy behavior across diverse physical systems. This is the heuristic picture associated with replica symmetry breaking (RSB) in…
We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order…
While gauge symmetry is a well-established requirement for representing topological orders in projected entangled-pair state (PEPS), its impact on the properties of low-lying excited states remains relatively unexplored. Here we perform…
The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these…
We examine a chain of periodic arrays of 4 quantum spins with magnitudes of 1/2, 1, 3/2 and 1. There are four kinds of nearest-neighbour exchange parameters among them. We choose two independent parameters for concreteness: one represents…
We consider general locally-interacting arbitrary-dimensional lattice spin systems that are gapped for any system size. We show under reasonable conditions that nondegenerate ground states of such systems obey the entanglement area law. In…
Motivated by recent discussions of the string-theory landscape, we propose field-theoretic realizations of models with large numbers of vacua. These models contain multiple U(1) gauge groups, and can be interpreted as deconstructed versions…
Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin-$1/2$…
Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many…
Spatial point process (SPP) models are commonly used to analyze point pattern data in many fields, including presence-only data in ecology. Existing exact Bayesian methods for fitting these models are computationally expensive because they…
This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both…
We investigate the behavior of shear viscosity in the presence of small anisotropy and a finite chemical potential. First, we construct an anisotropic Reissner Nordstr{\"o}m blackbrane in 5 dimensions in a simple Einstein-Maxwell theory…
The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions…