Related papers: An area law for 2D frustration-free spin systems
We present a model compound with a spin-1/2 frustrated square lattice, in which three ferromagnetic (F) interactions and one antiferromagnetic (AF) compet. Considering the effective spin-1 formed by the dominant F dimer, this square lattice…
Regulated Lorentz invariant quantum field theories satisfy an area law for the entanglement entropy $S$ of a spatial subregion in the ground state in $d>1$ spatial dimensions; nevertheless, the full density matrix contains many more than…
We study the asymptotic growth of the entanglement entropy of ground states of non-interacting (spinless) fermions in $\mathbb R^3$ subject to a non-zero, constant magnetic field perpendicular to a plane. As for the case with no magnetic…
A scalar field in the ground state, when partially hidden from observation by a spherical boundary, acquires entanglement entropy $S$ proportional to the area of the surface. This area law is well established in flat space, where it follows…
General local spin $S$ ground states, described by a Valence Bond Solid (VBS) on a two dimensional lattice are studied. The norm of these ground states is mapped to a classical O(3) model on the same lattice. Using this quantum-to-classical…
Magnetic properties of the transverse-field Ising model on curved (hyperbolic) lattices are studied by a tensor product variational formulation that we have generalized for this purpose. First, we identify the quantum phase transition for…
We study the entropy of a set of identical hard objects, of general shape, with each object pivoted on the vertices of a d-dimensional regular lattice of lattice spacing a, but can have arbitrary orientations. When the pivoting point is…
Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showing two results: first, we identify an approximate…
We examine the entanglement properties of the spin-half Heisenberg model on the two-dimensional square-lattice bilayer based on quantum Monte Carlo calculations of the second R\'enyi entanglement entropy. In particular, we extract the…
Using the conventional $T$-matrix approach, we discuss gapped phases in 1D, 2D, and 3D spin systems (both with and without a long range magnetic order) with bond disorder and with weakly interacting bosonic elementary excitations. This work…
We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of highly excited eigenstates of local Hamiltonians and of random pure…
We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high `entanglement energy' levels, from a flat band of levels with specific…
We would like to put the area law -- believed to by obeyed by entanglement entropies in the ground state of a local field theory -- to scrutiny in the presence of non-perturbative effects. We study instanton corrections to entanglement…
It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations. We show that even certain exponentially decaying correlations can imply gaplessness. This is exemplified by the…
We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with group-theoretical coherent states of the symplectic group…
We consider a family of translation-invariant quantum spin chains with nearest-neighbor interactions and derive necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit. More precisely, let $\psi$ be an…
We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation. In particular, we derive a general formula for the time dependent first order correction to…
We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global $\mathrm{SU}(2)$ symmetry, constrained to fixed total spin $J$ and magnetization $J_z = 0$. Focusing on spin-$\tfrac12$…
Various methods have been explored to prepare the spin-adapted ground state, the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-$z$ component. In such problem…
The scaling of entanglement entropy with subsystem size fails to distinguish between gapped and gapless ground state of a scalar field theory in $d>1$ dimensions. We show that the scaling of angular momentum resolved entanglement entropy…