Lattice gauge magnets: Local isospin from spin

Orland, Peter; Rohrlich, Daniel

doi:10.1016/0550-3213(90)90646-u

Cited by 152 publications

(178 citation statements)

References 29 publications

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“…We also like to thank P. Orland, who drew our attention to refs. [4,5,6], for very interesting discussions. One of the authors (U.-J.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…Such models were first constructed by Horn [4] in 1981. In 1990 they were rediscovered under the name of gauge magnets and investigated in more detail by Orland and Rohrlich [5,6]. 1 Having rediscovered these models another time, we go beyond the earlier work by showing how quantum link models are related to ordinary quantum field theories via dimensional reduction, and how they may be used to improve numerical simulations of QCD.…”

Section: Introductionmentioning

confidence: 99%

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Quantum link models: A discrete approach to gauge theories

1997

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We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as quantum spin models are related to ordinary classical spin systems. Here U(1) and SU(2) quantum link models are constructed explicitly. As Hamiltonian theories quantum link models are nonrelativistic gauge theories with potential applications in condensed matter physics. When formulated with a fifth Euclidean dimension, universality arguments suggest that dimensional reduction to four dimensions occurs. Hence, quantum link models are also reformulations of ordinary quantum field theories and are applicable to particle physics, for example to QCD. The configuration space of quantum link models is discrete and hence their numerical treatment should be simpler than that of ordinary lattice gauge theories with a continuous configuration space.

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“…We also like to thank P. Orland, who drew our attention to refs. [4,5,6], for very interesting discussions. One of the authors (U.-J.…”

Section: Acknowledgementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum link models: A discrete approach to gauge theories

1997

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“…Because SU (2) [77]. A quantum simulator for this system, using Rydberg atoms in an optical lattice, has been proposed in [73].…”

Section: Digital Quantum Simulator For An Su (2) Gauge Theorymentioning

confidence: 99%

“…In section 2, we begin with the simpler case of Abelian gauge theories. In order to address nonperturbative effects, we regularize the theory on a lattice, first following the classical Wilson formulation [51], and then extending the concept of lattice gauge theories to quantum link models [76][77][78][79]. The resulting Abelian gauge theories resemble models of condensed matter physics and quantum information theory.…”

Section: Introductionmentioning

confidence: 99%

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

2013

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Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

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“…While the first steps towards gauge theory quantum simulations will be taken in simpler gauge theories, quantum link models provide a long-term vision for how to eventually realize quantum simulations of QCD. The first U(1) and S U(2) gauge theories formulated with (generalized) quantum spins were constructed by Horn [49], and further investigated by Orland and Rohrlich under the name of gauge magnets [50]. Quantum link models [51,52,53] provide an alternative to Wilson's lattice gauge theory [54,55,56] for defining QCD beyond perturbation theory.…”

Section: Introductionmentioning

confidence: 99%

Towards quantum simulating QCD

Wiese

2014

Nuclear Physics A

104

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Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.

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Lattice gauge magnets: Local isospin from spin

Cited by 152 publications

References 29 publications

Quantum link models: A discrete approach to gauge theories

Quantum link models: A discrete approach to gauge theories

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

Towards quantum simulating QCD

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