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Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm

Publication ,  Journal Article
Liu, H; Chandrasekharan, S; Kaul, R
Published in: Physical Review D: Particles, Fields, Gravitation and Cosmology
November 30, 2020

We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the naïve U(2) symmetry is enhanced to SO(4). On the other hand our model has a novel spin-charge flip ℤC2 symmetry which is an important ingredient of free massless fermions. In this work we focus on one spatial dimension, and show that our model can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveu model. Our model remains solvable in the presence of the Hubbard coupling U, which maps to a combination of Gross-Neveu and Thirring couplings in one dimension. Using the meron-cluster algorithm we find that the ground state of our model is a valence bond solid when U=0. From our field theory analysis, we argue that the valence bond solid forms inevitably because of an interesting frustration between spin and charge sectors in the renormalization group flow enforced by the ℤC2 symmetry. This state spontaneously breaks translation symmetry by one lattice unit, which can be identified with a ℤχ2 chiral symmetry in the continuum. We show that increasing U induces a quantum phase transition to a critical phase described by the SU(2)1 Wess-Zumino-Witten theory. The quantum critical point between these two phases is known to exhibit a novel symmetry enhancement between spin and dimer. Here we verify the scaling relations of these correlation functions near the critical point numerically. Our study opens up the exciting possibility of numerical access to similar novel phase transitions in higher dimensions in fermionic lattice models using the meron-cluster algorithm.

Duke Scholars

Published In

Physical Review D: Particles, Fields, Gravitation and Cosmology

ISSN

1550-2368

Publication Date

November 30, 2020

Publisher

American Physical Society

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 5101 Astronomical sciences
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0201 Astronomical and Space Sciences
 

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Liu, H., Chandrasekharan, S., & Kaul, R. (2020). Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm (Submitted). Physical Review D: Particles, Fields, Gravitation and Cosmology.
Liu, Hanqing, Shailesh Chandrasekharan, and Ribhu Kaul. “Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm (Submitted).” Physical Review D: Particles, Fields, Gravitation and Cosmology, November 30, 2020.
Liu H, Chandrasekharan S, Kaul R. Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm (Submitted). Physical Review D: Particles, Fields, Gravitation and Cosmology. 2020 Nov 30;
Liu, Hanqing, et al. “Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm (Submitted).” Physical Review D: Particles, Fields, Gravitation and Cosmology, American Physical Society, Nov. 2020.
Liu H, Chandrasekharan S, Kaul R. Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm (Submitted). Physical Review D: Particles, Fields, Gravitation and Cosmology. American Physical Society; 2020 Nov 30;

Published In

Physical Review D: Particles, Fields, Gravitation and Cosmology

ISSN

1550-2368

Publication Date

November 30, 2020

Publisher

American Physical Society

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 5101 Astronomical sciences
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
  • 0201 Astronomical and Space Sciences