We present a minimal non-Hermitian model where topologically nontrivial complex energy spectrum is induced by inter-particle interactions. Our consists of one-dimensional chain with dynamical gauge field density dependence. The trivial for single particle system, but exhibits topology point gap when two or more particles are in the system. construct an effective doublon to describe presence particles, which quantitatively agrees full interacting model. can be realized modulating hoppings...

We theoretically investigate the nature of state at quarter filled lowest Landau level and predict that, as quantum well width is increased, a transition occurs from composite fermion Fermi sea into novel non-Abelian fractional Hall that topologically equivalent to $f$-wave pairing fermions. This distinct familiar $p$-wave paired Pfaffian state. compare our calculated phase diagram with experiments make predictions for many observable quantities.

A recent work [Balram, Jain, and Barkeshli, Phys. Rev. Res. 2, 013349 (2020)] has suggested that an unconventional state describing ${\mathbb{Z}}_{n}$ superconductivity of composite bosons, which supports excitations with charge $1/(3n)$ the electron charge, is energetically better than Laughlin wave function at $\ensuremath{\nu}=7/3$ in GaAs systems. All experiments to date, however, are consistent latter. To address this discrepancy, we study effect finite width on ground predict a phase...

The authors propose a plausible candidate for fractional quantum Hall effect at $\ensuremath{\nu}=2+3/7$ in the form of electrons as bound states fictitious partons, which themselves occupy integer states.

Theory predicts that double layer systems realize "two-component composite fermions," which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid crystal states as function the separation. Recent experiments in graphene have revealed large number layer-correlated fractional quantum Hall lowest Landau level, many not been studied quantitatively previous theoretical works. We consider competition between various at...

Recent systematic measurements of the quantum well width dependence excitation gaps fractional Hall states in high mobility samples [Villegas Rosales {\it et al.}, Phys. Rev. Lett. {\bf 127}, 056801 (2021)] open possibility a better quantitative understanding this important issue. We present what we believe to be accurate theoretical including effects finite and Landau level (LL) mixing. While theory captures dependence, there still remains deviation between calculated measured gaps,...

The nature of the fractional quantum Hall effect at $\ensuremath{\nu}=1/2$, observed in wide wells almost three decades ago, is still under debate. Previous studies have investigated it using variational Monte Carlo method, which assumes that transverse wave function and gap between symmetric antisymmetric subbands obtained a local density approximation zero magnetic field remain valid even high perpendicular fields; this method also ignores Landau level mixing. We develop work...

We investigate a discrete nonlinear Schr\"odinger equation with dynamical, density-difference-dependent gauge fields. find ground-state transition from plane wave condensate to localized soliton state as the coupling is varied. Interestingly we regime in which and are both stable. identify an emergent chiral symmetry, leads existence of symmetry-protected zero-energy edge mode. The symmetry relates low high energy solitons. These states indicate that interaction acts repulsively attractively.

Electron bilayers in a strong magnetic field exhibit insulating behavior for wide range of interlayer separation $d$ total Landau level fillings $\nu\leq 1/2$, which has been interpreted terms pinned crystal. We study theoretically the competition between many strongly correlated liquid and crystal states obtain phase diagram as function quantum well width several filling factors interest. predict that three structures can be realized: (a) At small $d$, Triangular Ising AntiFerromagnetic...

Many body localization (MBL) represents a unique physical phenomenon, providing testing ground for exploring thermalization, or more precisely its failure. Here we characterize the MBL phase geometrically by many-body quantum metric (MBQM), defined in parameter space of twist boundary. We find that MBQM scales linearly as function inverse system length phase, and grows faster ergodic phase. validate our theory using disordered hardcore Bose-Hubbard model, to transition via scale from MBQM....

We investigate a discrete non-linear Schr\"odinger equation with dynamical, density-difference-dependent, gauge fields. find ground-state transition from plane wave condensate to localized soliton state as the coupling is varied. Interestingly we regime in which and are both stable. identify an emergent chiral symmetry, leads existence of symmetry protected zero energy edge mode. The relates low high solitons. These states indicate that interaction acts repulsively attractively.

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