Simple Fermionic Model of Deconfined Phases and Phase Transitions

Abstract

Using quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with N flavors of fermions per site for N ¼ 1, 2, and 3. The models have an extensive number of conserved quantities but are not integrable, and they have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond the Landau-Ginzburg paradigm. In particular, one of the prominent phases for N > 1 corresponds to 2N gapless Dirac fermions coupled to an emergent Z 2 gauge field in its deconfined phase. However, unlike a conventional Z 2 gauge theory, we do not impose "Gauss's Law" by hand; instead, it emerges because of spontaneous symmetry breaking. Correspondingly, unlike a conventional Z 2 gauge theory in two spatial dimensions, our models have a finite-temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss's law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short-range entangled phase, which corresponds to Néel antiferromagnet or superconductor for N ¼ 2 and a valence-bond solid for N ¼ 3. Furthermore, for N ¼ 3, the valence-bond solid further undergoes a transition to a Néel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.

Orthogonal metal in the Hubbard model with liberated slave spins

“…As pointed out in Ref. [44], allQ i sectors are degenerate in this limit. This is not only true for the ground state, for which this fact was previously pointed out in Ref.…”

“…with the kinetic energy per bond (t = 1) and the superfluid density ρ s defined in Eq. (44). We find that Eq.…”

“…[31,33] that have no local symmetry and hence no associated Z 2 charge. It is also different from T = 0 numerical realizations of orthogonal (semi-)metals with spontaneously generated constraints [44,[74][75][76].…”

Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: A Monte Carlo study

“…Among others, QCPs related to the breaking of antiferromagnetic Z 2 [39,40] and XY [17,37], ferromagnetic Z 2 [41][42][43], charge density wave [21], and nematic [19][20][21]44] order have been investigated. Other recent studies focused on deconfined QCPs where fermionic matter fields are coupled to Z 2 [45][46][47][48] and U (1) [49] lattice gauge theories.…”

Self-learning quantum Monte Carlo method in interacting fermion systems

“…However, these systems are usually strongly correlated, and can only be solved by non-perturbative methods. In the last few years, after several attempts [7][8][9][10][11][12][13][14], people realize determinantal quantum Monte Carlo (DQMC) is one of the most suitable methods and sometimes even the only available choice. …”