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Register a new userA simple fermionic model of deconfined phases and phase transitions
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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.
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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 densities admit multiple competing charge-ordered insulating states with various periodicities and internal structure. Our reference point are systems with interaction range $p=2$, where phase transitions between these charge-ordered configurations are known to be mediated by liquid and bond-ordered phases. For increased interaction range $p=4$, we find that the phase transitions can also appear to be abrupt, as well as being mediated by re-emergent ordered phases that cross over into liquid behavior. These considerations are underpinned by a classification of the competing charge-ordered states in the atomic limit for varying interaction range at the principal commensurable particle densities. We also consider the effects of disorder, leading to fragmentization of the ordered phases and localization of the liquid phases.
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 invariants contain global information, in addition to the usual one (obtained by integrating the Berry connection around a closed loop). We compute these invariants (Chern numbers) and discuss their relation to QPT. In particular we show that Chern numbers can be used to label regions corresponding to different phases.
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 solid state physics: Landaus theories of Fermi liquids and phase transitions. We discuss two resulting exotic states of matter: topological and critical spin liquids. These two quantum phases do not display any long-range order even at zero temperature. In each case, we show how a gauge theory description is useful to describe the new concepts of topological order, fractionalization and deconfinement of excitations which can be present in such spin liquids. We make brief connections, when possible, to experiments in which the corresponding physics can be probed. Finally, we review recent work on deconfined quantum critical points. The tone of these lecture notes is expository: focus is on gaining a physical picture and understanding, with technical details kept to a minimum.
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-carrying non-equilibrium steady-state. We characterize the different non-equilibrium phases as functions of the chains parameters and magnetic potentials, in terms of their correlation functions and entanglement content. The mixed-order transition, recently observed for the particular case of a transverse field Ising chain, is established to emerge as a generic out-of-equilibrium feature and its critical exponents are determined analytically. Results are also contrasted with those obtained in the limit of Markovian reservoirs. Our findings should prove helpful in establishing the properties of non-equilibrium phases and phase transitions of extended open quantum systems.
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 of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS--AFM and AFM--cVBS boundaries merge into a direct sVBS--cVBS transition. Unlike previous models with putative deconfined AFM--cVBS transitions, e.g., the standard $J$-$Q$ model, in our extended $J$-$Q$ model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically $Z_4$ symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order the clock-like $Z_4$ fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries.
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