Related papers: Commuting Quantum Matrix Models
Magnetic insulators have proved to be fertile ground for studying new types of quantum many body states, and I survey recent experimental and theoretical examples. The insights and methods transfer also to novel superconducting and metallic…
We analyze relativistic quantum scattering in the Schr\"odinger picture. The suggestive requirement of translational invariance and conservation of the four-momentum, that the interacting Hamiltonian commute with the four-momentum $P$ of…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
Simulating the Hubbard model is of great interest to a wide range of applications within condensed matter physics, however its solution on classical computers remains challenging in dimensions larger than one. The relative simplicity of…
In this review, we study some aspects of the non-equilibrium dynamics of quantum systems. In particular, we consider the effect of varying a parameter in the Hamiltonian of a quantum system which takes it across a quantum critical point or…
Combined with Laughlin's argument on the quantized Hall conductivity, Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number, on a periodic lattice in…
We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…
We carry out the first step of a program conceived, in order to build a realistic model, having the particle spectrum of the standard model and renormalized masses, interaction terms and couplings, etc. which include the class of quantum…
It has been recently shown that small subsystems of finite quantum systems generically equilibrate. We extend these results to infinite-dimensional Hilbert spaces of field theories and matrix models. We consider a quench setup, where…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
As physical systems, qubits must evolve from input to output state. We describe a simple scheme in which the effect of a quantum gate is described by the action of an effective Hamiltonian acting for some characteristic time. This model…
We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
We investigate eigenvalue attraction for open quantum systems, biophysical systems, and for Parity-Time symmetric materials. To determine whether an eigenvalue and its complex conjugate of a real matrix attract, we derive expressions for…
The quantum propagator and characteristic equation in the presence of a chain of $\delta$-potentials are obtained in the rectangular, cylindrical and spherical coordinate systems. The simplicity and efficiency of the method is illustrated…