We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by-dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional-wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases.
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Due to rapidly improving quantum computing hardware, Hamiltonian simulations of relativistic lattice field theories have seen a resurgence of attention. This computational tool requires turning the formally infinite-dimensional Hilbert space of the full theory into a finite-dimensional one. For gauge theories, a widely used basis for the Hilbert space relies on the representations induced by the underlying gauge group, with a truncation that keeps only a set of the lowest dimensional representations. This works well at large bare gauge coupling, but becomes less efficient at small coupling, which is required for the continuum limit of the lattice theory. In this work, we develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. In particular, we show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved, which allows for this basis to be used at all values of the coupling. Little prior knowledge is assumed, so this may also be used as an introduction to the subject of Hamiltonian formulations of lattice gauge theories.
- Award ID(s):
- 2014071
- PAR ID:
- 10556983
- Publisher / Repository:
- Phys.Rev.D 109 (2024) 7, 074501
- Date Published:
- Journal Name:
- Physical Review D
- Volume:
- 109
- Issue:
- 7
- ISSN:
- 2470-0010
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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