Phase diagram and conformal string excitations of square ice using gauge invariant matrix product states

Tschirsich, Ferdinand; Montangero, Simone; Dalmonte, Marcello

doi:10.21468/scipostphys.6.3.028

Cited by 36 publications

(31 citation statements)

References 80 publications

(141 reference statements)

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“…Phase diagram and conformal string excitations of square ice using gauge invariant matrix product states [167] The examples discussed above widely demonstrate the computational capabilities of tensor network methods in dealing with (1+1)-d lattice gauge theories. Reference [167] reports instead results on a two-dimensional U(1) gauge theory, the (2+1)-d quantum link model, also known as square ice (for tensor network results on a theory with discrete gauge group, see Ref. [154]).…”

Section: 28mentioning

confidence: 92%

“…In this section, it is shown how tensor network techniques could go beyond Monte Carlo calculations, in the sense, of being able to perform real-time calculations and phase diagrams with finite density of fermions. Examples of these achievements appear in [138,[161][162][163][164][165][166][167].…”

Section: Phase Diagram and Dynamical Evolution Of Lattice Gauge Theormentioning

confidence: 99%

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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: 28mentioning

confidence: 92%

Section: Phase Diagram and Dynamical Evolution Of Lattice Gauge Theormentioning

confidence: 99%

Simulating lattice gauge theories within quantum technologies

et al. 2020

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“…Comparing the energy E(L D ) with the energy E 0 of the charge-free state, we obtain the string tension, S T (L D ) = E(L D ) − E 0 ( Fig. 4 (d)), which characterizes the confining properties [40].…”

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confidence: 99%

Deconfining Disordered Phase in Two-Dimensional Quantum Link Models

2020

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We explore the ground-state physics of two-dimensional spin-1/2 U (1) quantum link models, one of the simplest non-trivial lattice gauge theories with fermionic matter within experimental reach for quantum simulations. Whereas in the large mass limit we observe Neél-like vortex-antivortex and striped crystalline phases, for small masses there is a transition from the striped phases into a disordered phase whose properties resemble those at the Rokhsar-Kivelson point of the quantum dimer model. This phase is characterized on ladders by boundary Haldane-like properties, such as vanishing parity and finite string ordering. Moreover, from studies of the string tension between gauge charges, we find that whereas the stripe phases are confined, the novel disordered phase present clear indications of being deconfined. Our results open exciting perspectives of studying highly nontrivial physics in quantum simulators, such as spin-liquid behavior and confinement-deconfinement transitions, without the need of explicitly engineering plaquette terms. arXiv:1910.12829v1 [cond-mat.quant-gas]

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“…Direct DMRG study of quantum Z 2 LGT is difficult as realizing plaquette interactions consistently with the gauge symmetry is challenging. But such study is technically possible for Abelian and non-Abelian gauge theory in 2D by using symmetry-preserving tensor network techniques [69][70][71]. Interestingly, the duality between such a spin gauge theory and a generalized Ising model allows for scalable quantum simulation with Rydberg atoms [72].…”

Section: Jhep08(2020)160mentioning

confidence: 99%

“…As the next step regarding quantum and pseudoquantum simulations of LGT, we shall study Fermions coupled with the Z 2 gauge field using our method, on which the results can be compared with the existing results of QMC calculations, which are free of Fermion sign problem. Thereby the method can be further benchmarked, which can then be applied to other LGTs, for which Fermion sign problem exists in MC-based methods, as well as the LGTs that recently have been studied by using tensor network methods [69][70][71][72].…”

Section: Jhep08(2020)160mentioning

confidence: 99%

Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory

Cui

Shi

Yang

2020

J. High Energ. Phys.

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Gauge theory is the framework of the Standard Model of particle physics and is also important in condensed matter physics. As its major non-perturbative approach, lattice gauge theory is traditionally implemented using Monte Carlo simulation, consequently it usually suffers such problems as the Fermion sign problem and the lack of real-time dynamics. Hopefully they can be avoided by using quantum simulation, which simulates quantum systems by using controllable true quantum processes. The field of quantum simulation is under rapid development. Here we present a circuit-based digital scheme of quantum simulation of quantum Z 2 lattice gauge theory in 2 + 1 and 3 + 1 dimensions, using quantum adiabatic algorithms implemented in terms of universal quantum gates. Our algorithm generalizes the Trotter and symmetric decompositions to the case that the Hamiltonian varies at each step in the decomposition. Furthermore, we carry through a complete demonstration of this scheme in classical GPU simulator, and obtain key features of quantum Z 2 lattice gauge theory, including quantum phase transitions, topological properties, gauge invariance and duality. Hereby dubbed pseudoquantum simulation, classical demonstration of quantum simulation in state-of-art fast computers not only facilitates the development of schemes and algorithms of real quantum simulation, but also represents a new approach of practical computation.

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Phase diagram and conformal string excitations of square ice using gauge invariant matrix product states

Cited by 36 publications

References 80 publications

Simulating lattice gauge theories within quantum technologies

Simulating lattice gauge theories within quantum technologies

Deconfining Disordered Phase in Two-Dimensional Quantum Link Models

Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory

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