O(3) nonlinear sigma model in 
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 dimensions with matrix product states

Bruckmann, Falk; Jansen, Karl; Kühn, Stefan

doi:10.1103/physrevd.99.074501

Cited by 47 publications

(32 citation statements)

References 84 publications

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“…In particular, in recent years, there has been a boost in the development of tensor network methods to simulate lattice gauge theories. There are different approaches, that range from the exploitation of mappings of some theories to spin models [103,104], to the development of gauge invariant tensor networks in the quantum link formulation [22,23,101,[105][106][107]. This section reviews some of the studies that appeared in the last years, covering most of the available approaches for Abelian and non-Abelian lattice gauge theories [103][104][105][108][109][110][111].…”

Section: Quantum Information Techniques 41 Tensor Network For Lattimentioning

confidence: 99%

Simulating lattice gauge theories within quantum technologies

et al. 2020

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Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented-a classical simulation approachapplied to the study of lattice gauge theories together with some results on

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Section: Quantum Information Techniques 41 Tensor Network For Lattimentioning

confidence: 99%

Simulating lattice gauge theories within quantum technologies

et al. 2020

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“…The implementation of quantum simulators has been demonstrated using trapped ions [17] and ultracold atoms [18][19][20][21]. On the numerical side, there has been a lot of success in applying matrix product state methods to (1 + 1)-dimensional Abelian and non-Abelian lattice gauge theories [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], enabling the study of finite chemical potential scenarios and out-of-equilibrium dynamics which would not have been accessible in Monte Carlo simulations of Euclidean lattice gauge theory. Also, some generalizations of Gaussian states have proven to be suitable for these theories [37].…”

Section: Introductionmentioning

confidence: 99%

Real-time dynamics in 2+1D compact QED using complex periodic Gaussian states

Bender

Emonts

Zohar

et al. 2020

Phys. Rev. Research

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We introduce a class of variational states to study ground-state properties and real-time dynamics in (2 + 1)-dimensional compact QED. These are based on complex Gaussian states which are made periodic to account for the compact nature of the U (1) gauge field. Since the evaluation of expectation values involves infinite sums, we present an approximation scheme for the whole variational manifold. We calculate the ground-state energy density for lattice sizes up to 20 × 20 and extrapolate to the thermodynamic limit for the whole coupling region. Additionally, we study the string tension both by fitting the potential between two static charges and by fitting the exponential decay of spatial Wilson loops. As the ansatz does not require a truncation in the local Hilbert spaces, we analyze truncation effects which are present in other approaches. The variational states are benchmarked against exact solutions known for the one plaquette case and exact diagonalization results for a Z 3 lattice gauge theory. Using the time-dependent variational principle, we study real-time dynamics after various global quenches, e.g., the time evolution of a strongly confined electric field between two charges after a quench to the weak-coupling regime. Up to the points where finite-size effects start to play a role, we observe equilibrating behavior.

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“…Our truncation of the Hilbert space is also similar to Ref. [43], which makes the O(3) model amenable to tensor networks. Finally, our…”

Section: -2mentioning

confidence: 98%

σ Models on Quantum Computers

et al. 2019

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We formulate a discretization of σ models suitable for simulation by quantum computers. Space is substituted with a lattice, as usually done in lattice field theory, while the target space (a sphere) is replaced by the "fuzzy sphere", a construction well known from noncommutative geometry. Contrary to more naive discretizations of the sphere, in this construction the exact O(3) symmetry is maintained, which suggests that the discretized model is in the same universality class as the continuum model. That would allow for continuum results to be obtained for very rough discretizations of the target space as long as the space discretization is made fine enough. The cost of performing time evolution, measured as the number of controlled-NOT operations necessary, is 12LT=Δt, where L is the number of spatial sites, T the maximum time extent, and Δt the time spacing.

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O(3) nonlinear sigma model in 1+1 dimensions with matrix product states

Cited by 47 publications

References 84 publications

Simulating lattice gauge theories within quantum technologies

Simulating lattice gauge theories within quantum technologies

Real-time dynamics in 2+1D compact QED using complex periodic Gaussian states

σ Models on Quantum Computers

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