Tangent-space methods for uniform matrix product states

Vanderstraeten, Laurens; Haegeman, Jutho; Verstraete, Frank

doi:10.21468/scipostphyslectnotes.7

Cited by 186 publications

(204 citation statements)

References 83 publications

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“…For further details on uniform MPS, and in particular of the gauge fixing, we refer to the tangent-space review in Ref. [18]. Here we just mention that we always work in the mixed gauge and that the distortion tensor B obeys the left gauge-fixing condition…”

Section: Methodsmentioning

confidence: 99%

“…The formalism of translation-invariant matrix product states (MPS) in the thermodynamic limit-the so-called uniform MPS-has been developed for simulating static and dynamic properties of quantum spin chains [18]. In particular, it yields a natural description of elementary excitations as localized particles against a stronglycorrelated background [19].…”

Section: Spinons and Matrix Product Statesmentioning

confidence: 99%

“…and is translation invariant over n sites by construction. In recent years, it was shown that it is possible to variationally optimize over this set of states directly in the thermodynamic limit to find accurate ground-state approximations for a given hamiltonian [18,25]. The real power of MPS is laid bare when imposing symmetry constraints on the tensors that reflect the physical symmetries in the system.…”

Section: Spinons and Matrix Product Statesmentioning

confidence: 99%

“…15 and 41 spinon confinement in spin-1/2 chains was already simulated using the framework of uniform MPS without symmetries. In the following we have performed the simulations using tangent-space methods for uniform MPS [18] using full SU(2)-symmetric tensor-network operations [45].…”

Section: Spinons and Their Confinement In The Spin-1 Chainmentioning

confidence: 99%

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Spinon confinement and deconfinement in spin-1 chains

et al. 2020

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We explain how spinons and magnons naturally arise in SU(2) invariant spin chains when describing ground states and elementary excitations using MPS. Within this description, spinons can emerge in a spin-1 chain at a first-order transition between a symmetry-protected topological phase and a trivial phase. We provide MPS simulations for the spinon dispersion relations in a frustrated and dimerized spin-1 chain, and show that these spinons determine the low-lying spectrum in the vicinity of this transition by the formation of spinon/anti-spinon bound states.

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Section: Methodsmentioning

confidence: 99%

Section: Spinons and Matrix Product Statesmentioning

confidence: 99%

Section: Spinons and Matrix Product Statesmentioning

confidence: 99%

Section: Spinons and Their Confinement In The Spin-1 Chainmentioning

confidence: 99%

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Spinon confinement and deconfinement in spin-1 chains

et al. 2020

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“…For the sake of completeness, we review here the fundamental aspects of the main techniques employed in the context of lattice gauge theories, and we refer the reader to the literature on the subject for detailed technical descriptions of the algorithms (see, e.g., Refs. [203,204,206,[244][245][246][247][248]). Most of the algorithms we describe here are easy to implement, and there exist several libraries available to the public that currently provide most of the functionality [249][250][251][252].…”

Section: Main Numerical Algorithmsmentioning

confidence: 99%

Review on novel methods for lattice gauge theories

2020

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Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem.In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.

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Tensor Network Contractions

Ran

Tirrito

Peng

et al. 2020

Lecture Notes in Physics

112

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PrefaceTensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum information science, statistical physics, and so on. In this lecture notes, we focus on the contraction algorithms of TN as well as some of the applications to the simulations of quantum many-body systems. Starting from basic concepts and definitions, we first explain the relations between TN and physical problems, including the TN representations of classical partition functions, quantum many-body states (by matrix product state, tree TN, and projected entangled pair state), time evolution simulations, etc. These problems, which are challenging to solve, can be transformed to TN contraction problems. We present then several paradigm algorithms based on the ideas of the numerical renormalization group and/or boundary states, including density matrix renormalization group, time-evolving block decimation, coarsegraining/corner tensor renormalization group, and several distinguished variational algorithms. Finally, we revisit the TN approaches from the perspective of multilinear algebra (also known as tensor algebra or tensor decompositions) and quantum simulation. Despite the apparent differences in the ideas and strategies of different TN algorithms, we aim at revealing the underlying relations and resemblances in order to present a systematic picture to understand the TN contraction approaches. v AcknowledgementsWe are indebted to

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Tangent-space methods for uniform matrix product states

Cited by 186 publications

References 83 publications

Spinon confinement and deconfinement in spin-1 chains

Spinon confinement and deconfinement in spin-1 chains

Review on novel methods for lattice gauge theories

Tensor Network Contractions

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