Gross–Neveu–Wilson model and correlated symmetry-protected topological phases

Bermúdez, A.; Tirrito, Emanuele; Rizzi, Matteo; Lewenstein, Maciej; Hands, Simon

doi:10.1016/j.aop.2018.10.007

Cited by 49 publications

(82 citation statements)

References 141 publications

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“…2 (a). We note that a similar splitting of a c = 1 massless Dirac fermion into a couple of c = 1/2 massless Majoranas has been recently observed in other models of correlated SPT phases with instantaneous Hubbard-type interactions instead of the gauge-mediated ones [58][59][60]. In this section, we consider the following question: what is the fate of the SPT phase as we increase the dimension of the gauge group symmetry Z N ?…”

Section: B Lattice Discretization Of the Schwinger Modelmentioning

confidence: 69%

ZN gauge theories coupled to topological fermions: QED2 with a quantum mechanical θ angle

et al. 2019

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We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes (1+1) quantum electrodynamics of an Abelian U(1) gauge field coupled to a symmetry-protected topological matter sector, by means of a class of Z N lattice gauge theories. Employing density-matrix renormalization group techniques that exactly implement Gauss' law, we show that these models host a correlated topological phase for different values of N, where fermion correlations arise through inter-particle interactions mediated by the gauge field. Moreover, by a careful finite-size scaling, we show that this phase is stable in the large-N limit, and that the phase boundaries are in accordance to bosonization predictions of the U(1) topological Schwinger model. Our results demonstrate that Z N finite-dimensional gauge groups offer a practical route for an efficient classical simulation of equilibrium properties of electromagnetism with topological fermions. Additionally, we describe a scheme for the quantum simulation of a topological Schwinger model exploiting spin-changing collisions in boson-fermion mixtures of ultra-cold atoms in optical lattices. Although technically challenging, this quantum simulation would provide an alternative to classical density-matrix renormalization group techniques, providing also an efficient route to explore real-time non-equilibrium phenomena. :1906.07005v1 [cond-mat.quant-gas] CONTENTS arXiv

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Section: B Lattice Discretization Of the Schwinger Modelmentioning

confidence: 69%

ZN gauge theories coupled to topological fermions: QED2 with a quantum mechanical θ angle

et al. 2019

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“…(4) and by comparing h G α (k) with h S α (k), we expect that in the i-SSH model, the same mechanism leads to a modification of the parameter J 1 , that is, interaction acts as correction for the parameter J 1 , which determines the strength of the inner-bond order in the i-SSH model. Some previous studies [6,14] have expected that the CGNW model has a novel state with a non-zero expectation value ofψ α,i γ 5 ψ α,i in a large g 2 regime. This state is known as the Aoki phase, which is a parity-broken phase [5,6,14].…”

Section: Relationshipmentioning

confidence: 97%

“…Some previous studies [6,14] have expected that the CGNW model has a novel state with a non-zero expectation value ofψ α,i γ 5 ψ α,i in a large g 2 regime. This state is known as the Aoki phase, which is a parity-broken phase [5,6,14]. Then, from the relation of Eq.…”

Section: Relationshipmentioning

confidence: 97%

“…These relations indicate that the inner-bond operator in the i-SSH model corresponds to the particle-anti-particle pairing operator in the CGNW model and the densitydifference operator between the left and right inner site in a unit cell to the pseudo-scalar operator, which corresponds to a pion field and whose expectation value characterizes a pion condensation in the high-energy physics context [4,6].…”

Section: Relationshipmentioning

confidence: 99%

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Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice

Kuno

2019

Phys. Rev. B

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The N -flavor interacting Su-Schrieffer-Heeger (i-SSH) model realizable in cold-atoms in an optical lattice is studied. We clarify the relationship between the i-SSH model and the Chiral-Gross-Neveu-Wilson (CGNW) model. Following the previous study of the CGNW model in the high-energy physics community, the groundstate phases of the i-SSH model are investigated and interpreted from the view of the phases of the CGNW model. The interaction effect on the i-SSH model, belonging to the topological BDI class, is grasped by following the view of the dynamical breakdown of chiral symmetry in the CGNW model. Furthermore, we compare the large-N groundstate phase diagram with that of the N = 1 case obtained by exact diagonalization and then propose a table-top cold-atom quantum simulator to test the model.

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“…In Ref. [64], the phase diagram is studied for anistropic lattices in order to understand the result of density-matrix renormalizatoin group, and it is found that Aoki phase does not extend to the zero coupling when lattice anistropy is introduced. This is consistent with our anomaly constraint since lattice π 2 rotation is explicitly broken, which clarifies the importance of lattice symmetries.…”

Section: Aoki Phase Of 2d Lattice Gross-neveu Model With Wilson Fermionmentioning

confidence: 99%

Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion

Misumi

Tanizaki

2020

Progress of Theoretical and Experimental Physics

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We develop the (1 + 1)d lattice U (1) gauge theory in order to define 2-flavor massless Schwinger model, and discuss its connection with Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, m, and the Wilson parameter, r, as m + 2r = 0. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of m is required because the extra U (1) symmetry at the central branch, U (1) V , prohibits the additive mass renormalization. Moreover, we show that Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so the Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we show that this lattice model has the mixed 't Hooft anomaly between U (1) V , lattice translation, and lattice rotation. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of Haldane conjecture. Furthermore, it gives new and strict understanding on parity-broken phase (Aoki phase) of 2d Wilson fermion.

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Gross–Neveu–Wilson model and correlated symmetry-protected topological phases

Cited by 49 publications

References 141 publications

ZN gauge theories coupled to topological fermions: QED2 with a quantum mechanical θ angle

ZN gauge theories coupled to topological fermions: QED2 with a quantum mechanical θ angle

Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice

Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion

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