Tensor renormalization group study of the non-Abelian Higgs model in two dimensions

Bazavov, A.; Catterall, Simon; Jha, Raghav G.; Unmuth-Yockey, Judah

doi:10.1103/physrevd.99.114507

Cited by 58 publications

(39 citation statements)

References 32 publications

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“…General studies of the structure and properties of PEPS with local gauge symmetries were discussed in [108,109,[111][112][113][114][115]. In addition, there has also been an effort specifically focused on classical tensor network methods with Grassmann fields [116][117][118][119][120][121], investigation of the sign problem tackled with TN and compared with Monte Carlo [122], works on the O(2) model with a purely imaginary chemical potential using TN [123,124], or on exploiting useful mappings to construct tensors and study lattice field theories [125][126][127][128][129][130][131][132].…”

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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“…When one applies the TRG to a gauge theory with a continuous group using the character expansion, the dimension of the original fundamental tensor is infinite because there are infinitely many representations. In the case of U(1) and SU(2) gauge groups, which have been studied so far in the literature [24][25][26][27], there is a natural choice for restricting the number of representations because the representation is labeled by the charge and the spin, respectively. Obviously, this issue becomes more nontrivial in the case of SU(N ) and U(N ) gauge groups with N ≥ 3.…”

Section: Application To U(n ) and Su(n ) Gauge Theoriesmentioning

confidence: 99%

“…One of the remaining issues in the TRG is the application to gauge theories, which is so far limited to U(1) and SU (2) gauge groups [24][25][26][27]. In view of this situation, here we discuss its application to U(N ) and SU(N ) gauge theories using the character expansion to rewrite the group integral as a sum over discrete indices.…”

Section: Introductionmentioning

confidence: 99%

Tensor renormalization group and the volume independence in 2D U(N) and SU(N) gauge theories

Hirasawa

Matsumoto

Nishimura

et al. 2021

J. High Energ. Phys.

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The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. One of the remaining issues is the application to gauge theories, which is so far limited to U(1) and SU(2) gauge groups. In the case of higher rank, it becomes highly nontrivial to restrict the number of representations in the character expansion to be used in constructing the fundamental tensor. We propose a practical strategy to accomplish this and demonstrate it in 2D U(N) and SU(N) gauge theories, which are exactly solvable. Using this strategy, we obtain the singular-value spectrum of the fundamental tensor, which turns out to have a definite profile in the large-N limit. For the U(N) case, in particular, we show that the large-N behavior of the singular-value spectrum changes qualitatively at the critical coupling of the Gross-Witten-Wadia phase transition. As an interesting consequence, we find a new type of volume independence in the large-N limit of the 2D U(N) gauge theory with the θ term in the strong coupling phase, which goes beyond the Eguchi-Kawai reduction.

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“…It is known how to map gauge theories into tensor networks by following the procedure described in e.g., [49]. This method, based on character expansion of the group valued action, will be described in detail in Sec.…”

Section: Review Of the Palatini-cartan Formulation Of Einstein Grmentioning

confidence: 99%

“…The review [48] compares the differences and strengths of these different algorithms. Tensor network formulations have had some success in analyzing many spin and lattice gauge models [49][50][51][52] but this paper constitutes the first attempt to use them to study quantum gravity.…”

Section: Introductionmentioning

confidence: 99%

Tensor network formulation of two-dimensional gravity

2020

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We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to twodimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We then augment the action with a Yang-Mills term which allows us to control the lattice spacing and show how to apply the tensor renormalization group to compute the free energy and look for critical behavior. Finally we perform an analytic continuation in the gravity coupling in this extended model and show that its critical behavior in a certain scaling limit depends only on the topology of the underlying lattice. We also show how the lattice gauge theory can be naturally generalized to generate the Polyakov or Liouville action for two dimensional quantum gravity.

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Tensor renormalization group study of the non-Abelian Higgs model in two dimensions

Cited by 58 publications

References 32 publications

Simulating lattice gauge theories within quantum technologies

Simulating lattice gauge theories within quantum technologies

Tensor renormalization group and the volume independence in 2D U(N) and SU(N) gauge theories

Tensor network formulation of two-dimensional gravity

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