Condensed Matter Theory

Abstract:

We introduce a new variational wave function for a quantum Hall bilayer at total filling νT=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length. The s-wave trial wave function naturally allows for charge imbalance between the layers and provides important insights into how the physics at large interlayer separations crosses over to that at small separations in a fashion analogous to the BEC-BCS crossover.

Abstract:

Rydberg chains provide an appealing platform for probing conformal field theories (CFTs) that capture universal behavior in a myriad of physical settings. Focusing on a Rydberg chain at the Ising transition separating charge density wave and disordered phases, we establish a detailed link between microscopics and low-energy physics emerging at criticality. We first construct lattice incarnations of primary fields in the underlying Ising CFT including chiral fermions, a nontrivial task given that the Rydberg chain Hamiltonian does not admit an exact fermionization. With this dictionary in hand, we compute correlations of microscopic Rydberg operators, paying special attention to finite, open chains of immediate experimental relevance. We further develop a method to quantify how second-neighbor Rydberg interactions tune the sign and strength of four-fermion couplings in the Ising CFT. Finally, we determine how the Ising fields evolve when four-fermion couplings drive an instability to Ising tricriticality. Our results pave the way to a thorough experimental characterization of Ising criticality in Rydberg arrays, and can inform the design of novel higher-dimensional phases based on coupled critical chains.

Abstract:

We argue and numerically substantiate that the real-space entanglement spectrum (RSES) of chiral Abelian quantum Hall states is given by the spectrum of a local boundary perturbation of a (1+1)-dimensional conformal field theory, which describes an effective edge dynamics along the real-space cut. The cut-and-glue approach suggests that the low-lying RSES is equivalent to the low-lying modes of some effective edge action. The general structure of this action is deduced by mapping to a boundary critical problem, generalizing the work of Dubail, Read, and Rezayi [Phys. Rev. B 85, 115321 (2012)]. Using trial wave functions, we numerically test our model of the RSES for the ν=2/3 bosonic composite fermion state.

Abstract:

By varying the disorder realization in the many-body localized (MBL) phase, we investigate the influence of resonances on spectral properties. The standard theory of the MBL phase is based on the existence of local integrals of motion (LIOM), and eigenstates of the time evolution operator can be described as LIOM configurations. We show that smooth variations of the disorder give rise to avoided level crossings, and we identify these with resonances between LIOM configurations. Through this parametric approach, we develop a theory for resonances in terms of standard properties of nonresonant LIOM. This framework describes resonances that are locally pairwise, and is appropriate in arbitrarily large systems deep within the MBL phase. We show that resonances are associated with large level curvatures on paths through the ensemble of disorder realizations, and we determine the curvature distribution. By considering the level repulsion associated with resonances, we calculate the two-point correlator of the level density. We also find the distributions of matrix elements of local observables and discuss implications for low-frequency dynamics.