相关论文: Knabe's spectral gap method for open boundary cond…
We study finite-time spectral rigidity in reversible Markov chains via exact spectral relaxation dynamics. While the underlying identities follow classically from self-adjointness on $L^2(\pi)$, organizing the dynamics around the relaxation…
Approach to the thermodynamic limit of a non-relativistic ideal gas in a periodic box is investigated. The single particle wave function obeys twisted boundary condition, $\psi(L)=e^{i\theta}\psi(0)$ for which the free particle spectrum is…
Recently, there has been growing interest in employing condensed matter systems such as quantum spin or harmonic chains as quantum channels for short distance communication. Many properties of such chains are determined by the spectral gap…
We consider holographic theories at finite temperature in which a continuous global symmetry in the bulk is spontaneously broken. We study the linear response of operators in a regime which is dual to time dependent, long wavelength…
This paper develops a new framework, \emph{simultaneous saturation}, designed to quantify the size of sets whose elements are simultaneously large. The framework establishes a correspondence between the magnitude of such sets and a system…
We prove that the spectral gap of the spin-1/2 ferromagnetic XXZ chain with Hamiltonian $H=-\sum_x S^{(1)}_xS^{(1)}_{x+1}+S^{(2)}_xS^{(2)}_{x+1} +\Delta S^{(3)}_xS^{(3)}_{x+1}$, is given by $\Delta-1$ for all $\Delta\geq 1$. This is the gap…
The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…
Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified…
Validity of modified finite-size scaling above the upper critical dimension is demonstrated for the quantum phase transition whose dynamical critical exponent is $z=2$. We consider the $N$-component Bose-Hubbard model, which is exactly…
We analyze a class of quantum spin models defined on half-spaces in the $d$-dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector $m\in\mathbb{R}^d$. The family of models was previously introduced as the…
Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition. The key point of our method is that there exist some degenerate points of…
A simple and reliable finite difference approach is presented for solution of the Dirac equation eigenproblem for states confined in rotationally symmetric systems. The method sets the boundary condition for the spinor wave function…
We apply the Sklyanin method of separation of variables to the reflection algebra underlying the open spin-1/2 XXX chain with non-diagonal boundary fields. The spectral problem can be formulated in terms of a TQ-equation which leads to the…
We consider an exactly solvable inhomogeneous Dicke model which describes an interaction between a disordered ensemble of two-level systems with single mode boson field. The existing method for evaluation of Richardson-Gaudin equations in…
Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one…
The $\mathbf{k \cdot p}$ method is a successful approach to obtain band structure, optical and transport properties of semiconductors, and it depends on external parameters that are obtained either from experiments, tight binding or ab…
We study the nonadiabatic dynamics of a two-dimensional higher-order topological insulator when the system is slowly quenched across the boundary-obstructed phase transition, which is characterized by edge band gap closing. We find that the…
Finite-temperature properties of the frustrated Hubbard model are theoretically examined by using the recently proposed thermal pure quantum state, which is an unbiased numerical method for finite-temperature calculations. By performing…
Finite-size scaling expressions for the current near the continuous phase transition, and for the local density near the first-order transition, are found in the steady state of the one-dimensional fully asymmetric simple-exclusion process…
The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their…