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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 $N=1,2$ and $3$. The models have an extensive number of conserved quantities but are not integrable, and have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond Landau-Ginzburg paradigm. In particular, one of the prominent phase for $N>1$ corresponds to $2N$ gapless Dirac fermions coupled to an emergent $mathbb{Z}_2$ gauge field in its deconfined phase. However, unlike a conventional $mathbb{Z}_2$ gauge theory, we do not impose the `Gausss Law by hand and instead, it emerges due to spontaneous symmetry breaking. Correspondingly, unlike a conventional $mathbb{Z}_2$ 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 Gausss law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short range entangled phase, which corresponds to Neel/Superconductor for $N=2$ and a Valence Bond Solid for $N=3$. Furthermore, for $N=3$, the Valence Bond Solid further undergoes a transition to a Neel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.
We identify ground states of one-dimensional fermionic systems subject to competing repulsive interactions of finite range, and provide phenomenological and fundamental signatures of these phases and their transitions. Commensurable particle densitie
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These inva
We present a pedagogical overview of recent theoretical work on unconventional quantum phases and quantum phase transitions in condensed matter systems. Strong correlations between electrons can lead to a breakdown of two traditional paradigms of sol
We obtain the steady-state phase diagram of a transverse field XY spin chain coupled at its ends to magnetic reservoirs held at different magnetic potentials. In the long-time limit, the magnetization bias across the system generates a current-carryi
We use quantum Monte Carlo simulations to study a quantum $S=1/2$ spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Neel antiferromagnet (AFM), as in the scenario