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Related papers: An area law for 2D frustration-free spin systems

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We study the time dependence of R\'{e}nyi/entanglement entropies of locally excited states created by fields with integer spins $s \leq 2$ in $4$ dimensions. For spins 0, 1 these states are characterised by localised energy densities of a…

High Energy Physics - Theory · Physics 2023-04-26 Justin R. David , Jyotirmoy Mukherjee

The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit an enormously rich…

Quantum Physics · Physics 2007-05-23 F. Verstraete , M. M. Wolf , D. Perez-Garcia , J. I. Cirac

An exact mechanism is written down to guarantee extensive residual ground state entropy and spin liquidity in spin-1/2 lattice models with bond-dependent couplings. It is based on the presence of extensively large and mutually non-commuting…

Statistical Mechanics · Physics 2025-08-15 Sumiran Pujari

Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians, as they inherently satisfy the boundary law of entanglement entropy. In this…

Strongly Correlated Electrons · Physics 2025-05-14 Daniel Alcalde Puente , Erik Lennart Weerda , Konrad Schröder , Matteo Rizzi

It is known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundaries. In this paper, we demonstrate how coarse-graining over these states can lead to an entanglement entropy. In particular,…

High Energy Physics - Theory · Physics 2009-10-28 A. P. Balachandran , L. Chandar , Arshad Momen

We ask whether a local Hamiltonian with a featureless (fully gapped and nondegenerate) ground state could exist in certain quantum spin systems. We address this question by mapping the vicinity of certain quantum critical point (or gapless…

Strongly Correlated Electrons · Physics 2018-02-21 Chao-Ming Jian , Zhen Bi , Cenke Xu

We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of…

Strongly Correlated Electrons · Physics 2007-05-23 Jean Richert

For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate…

While highly entangled ground states of gapless local Hamiltonians have been known to exist in one dimension, their two-dimensional counterparts were only recently found, with rather sophisticated interactions involving at least four…

Quantum Physics · Physics 2025-12-16 Zhao Zhang , Olai B. Mykland

We study properties of the minimal surface in the Area Law Solution \cite{M93}, \cite{M19a}, \cite{M19b}. We find out that Area Law holds exactly for 2D turbulence as well as for arbitrary planar loop in higher dimensions. This relies on…

High Energy Physics - Theory · Physics 2019-06-28 Alexander Migdal

We construct a class of projected entangled pair states (PEPS) which is exactly the resonating valence bond (RVB) wavefunctions endowed with both short range and long range valence bonds. With an energetically preferred RVB pattern, the…

Strongly Correlated Electrons · Physics 2013-07-22 Ling Wang , Didier Poilblanc , Zheng-Cheng Gu , Xiao-Gang Wen , Frank Verstraete

We consider entanglement entropy between two halves of space separated by a plane, in the theory of free photon in 3+1 dimensions. We show how to separate local gauge invariant quantities that belong to the two spatial regions. We calculate…

High Energy Physics - Theory · Physics 2020-08-05 Candost Akkaya , Alex Kovner

Suppose we would like to approximate all local properties of a quantum many-body state to accuracy $\delta$. In one dimension, we prove that an area law for the Renyi entanglement entropy $R_\alpha$ with index $\alpha<1$ implies a matrix…

Quantum Physics · Physics 2019-03-26 Yichen Huang

Magnetic frustration is a route that can lead to the emergence of novel ground states, including spin liquids and spin ices. Such frustration can be introduced through either the geometry of lattice structures or by incompatible exchange…

We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded…

Quantum Physics · Physics 2017-12-06 Ramis Movassagh

We investigate the entanglement properties of multi-mode Gaussian states, which have some symmetry with respect to the ordering of the modes. We show how the symmetry constraints the entanglement between two modes of the system. In…

Quantum Physics · Physics 2009-11-10 M. M. Wolf , F. Verstraete , J. I. Cirac

We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that…

Strongly Correlated Electrons · Physics 2012-07-24 M. B. Hastings

We show the violation of the entanglement-area law for bosonic systems with Bose surfaces. For bosonic systems with gapless factorized energy dispersions on a N^d Cartesian lattice in d-dimension, e.g., the exciton Bose liquid in two…

Quantum Physics · Physics 2013-12-03 Hsin-Hua Lai , Kun Yang , N. E. Bonesteel

We introduce a method based on semidefinite programming that produces rigorous two-sided bounds on ground state energy densities and correlation functions of translation-invariant classical spin models on infinite lattices. In this method,…

Statistical Mechanics · Physics 2026-05-11 Nisarga Paul , Gil Refael

Average block entanglement in the 1D XX-model with uncorrelated random couplings is known to grow as the logarithm of the block size, in similarity to conformal systems. In this work we study random spin chains whose couplings present long…

Statistical Mechanics · Physics 2016-07-19 Javier Rodríguez-Laguna , Silvia N. Santalla , Giovanni Ramírez , Germán Sierra