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We study planar two-dimensional quantum systems on a lattice whose Hamiltonian is a sum of local commuting projectors of bounded range. We consider whether or not such a system has a zero energy ground state. To do this, we consider the…

Quantum Physics · Physics 2016-12-15 M. B. Hastings

An algorithm is proposed for constructing quasi-random "peaked" quantum circuits, i.e., circuits whose final qubit state exhibits a high probability concentration on a specific computational basis state. These circuits consist of random…

Quantum Physics · Physics 2025-08-12 O. G. Udalov

The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough paper [F. Verstraete, J.I. Cirac, Phys. Rev. Lett. 104, 190405(2010)], provides a powerful variational ansatz for the ground state of…

Strongly Correlated Electrons · Physics 2017-06-07 Martin Ganahl , Julian Rincon , Guifre Vidal

Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…

We present a variational matrix product state (vMPS) for the ground state of the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer configurations, in faithful reflection of the resonating valence bond (RVB) picture…

Strongly Correlated Electrons · Physics 2021-04-07 Jintae Kim , Minsoo Kim , Pramod Padmanabhan , Jung Hoon Han , Hyun-Yong Lee

We consider general classes of gradient models on regular trees with values in a countable Abelian group $S$ such as $\mathbb{Z}$ or $\mathbb{Z}_q$, in regimes of strong coupling (or low temperature). This includes unbounded spin models…

Probability · Mathematics 2024-07-25 Alberto Abbondandolo , Florian Henning , Christof Kuelske , Pietro Majer

One-way quantum computation proceeds by sequentially measuring individual spins (qubits) in an entangled many-spin resource state. It remains a challenge, however, to efficiently produce such resource states. Is it possible to reduce the…

Quantum Physics · Physics 2010-11-03 Jonathan Lavoie , Rainer Kaltenbaek , Bei Zeng , Stephen D. Bartlett , Kevin J. Resch

We study AKLT models on locally tree-like lattices of fixed connectivity and find that they exhibit a variety of ground states depending upon the spin, coordination and global (graph) topology. We find a) quantum paramagnetic or valence…

Disordered Systems and Neural Networks · Physics 2010-05-24 C. R. Laumann , S. A. Parameswaran , S. L. Sondhi , F. Zamponi

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic Asymmetric Simple Exclusion Process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not…

Statistical Mechanics · Physics 2018-06-13 Eric Bertin , Matthieu Vanicat

Systems of correlated quantum matter can be a steep challenge to any would-be method of solution. Matrix-product state (MPS)-based methods can describe 1D systems quasiexactly, but often struggle to retain sufficient bipartite entanglement…

Strongly Correlated Electrons · Physics 2024-11-04 Gunnar Bollmark , Sam Mardazad , Johannes S. Hofmann , Adrian Kantian

We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density…

Strongly Correlated Electrons · Physics 2007-05-23 F. Verstraete , J. I. Cirac

Gapped ground states of quantum spin systems have been referred to in the physics literature as being `in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on $s \in [0,1]$,…

Mathematical Physics · Physics 2012-03-13 Sven Bachmann , Spyridon Michalakis , Bruno Nachtergaele , Robert Sims

In this paper we consider nearest neighbour models where the spin takes values in the set $\Phi=\{\z_1,\z_2,...,\z_q\}$ and is assigned to the vertices of the Cayley tree ${\G}^k$. The Hamiltonian is defined by some given…

Operator Algebras · Mathematics 2007-05-23 Francesco Fidaleo , Farruh Mukhamedov

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…

Quantum Physics · Physics 2015-09-10 Sergey Bravyi , David Gosset

Utilizing the framework of matrix product states, we investigate gauging as a method for exploring quantum phases of matter. Specifically, we describe how symmetry-protected topological (SPT) phases and spontaneous symmetry breaking (SSB)…

Quantum Physics · Physics 2025-09-08 David Blanik , José Garre-Rubio , Norbert Schuch

Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…

Quantum Physics · Physics 2026-02-10 Yong Liu , Guangyao Huang , Yizhi Wang , Junjie Wu

Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state…

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…

Quantum Physics · Physics 2007-08-02 D. Perez-Garcia , F. Verstraete , M. M. Wolf , J. I. Cirac

We present a general construction of matrix product states for stationary density matrices of one-dimensional quantum spin systems kept out of equilibrium through boundary Lindblad dynamics. As an application we review the isotropic…

Mathematical Physics · Physics 2016-12-13 D. Karevski , V. Popkov , G. M. Schütz

We prove that a quantum spin chain with half-odd-integral spin cannot have a unique ground state with a gap, provided that the interaction is short ranged, translation invariant, and possesses time-reversal symmetry or ${\mathbb Z}_2 \times…

Mathematical Physics · Physics 2019-02-20 Yoshiko Ogata , Hal Tasaki