Related papers: Boundary conditions for quantum lattice systems
I review the role of Lieb-Robinson bounds in characterizing and utilizing the locality properties of the Heisenberg dynamics of quantum lattice systems. In particular, I discuss two definitions of gapped ground state phases and show that…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…
We introduce reinforcement learning (RL) formulations of the problem of finding the ground state of a many-body quantum mechanical model defined on a lattice. We show that stoquastic Hamiltonians - those without a sign problem - have a…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
We shall show that the abstract and formal rules which govern the quantum kinematic and dynamics can be derived from a law of change of the information content or the degree of uncertainty that the system has a certain configuration in a…
We consider a general class of spatially local non-Markovian open quantum lattice models, with a bosonic environment that is approximated as Gaussian. Under the assumption of a finite environment memory time, formalized as a finite total…
We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical…
We construct topological defects in two-dimensional classical lattice models and quantum chains. The defects satisfy local commutation relations guaranteeing that the partition function is independent of their path. These relations and…
A large class of quantum phase transitions for quantum lattice systems are characterized by local order parameters. It is shown that local order parameters may be systematically constructed from tensor network representations of quantum…
We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the…
We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field…
We investigate Luttinger junctions of quantum wires away from criticality. The one-body scattering matrix, corresponding to the off-critical boundary conditions at the junction, admits in general antibound and/or bound states. Their…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
We introduce ``local uncertainty relations'' in thermal many-body systems, from which fundamental bounds in quantum systems can be derived. These lead to universal non-relativistic speed limits (independent of interaction range) and…
A cosmology inspired structure for phase space is introduced, which leads to finitization and lattice-like discretization of position and momentum eigenvalues in a preferred, cosmic frame. Lorentz invariance is broken at very high energies,…
The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all…
We present a general theoretical framework for finding the time-optimal unitary evolution of the quantum systems when the Hamiltonian is subject to arbitrary constraints. Quantum brachistochrone (QB) is such a framework based on the…
The standard notion of a classical limit, represented schematically by $\hbar\rightarrow 0$, provides a method for approximating a quantum system by a classical one. In this work we explain why the standard classical limit fails when…