Person:

Strack, Philipp

We study models of itinerant spinless fermions with random long-range interactions. We motivate such models from descriptions of fermionic atoms in multimode optical cavities. The solution of an infinite-range model yields a metallic phase, which has glassy charge dynamics, and a localized glass phase with suppressed density of states at low energies. We compare these phases to the conventional disordered Fermi liquid, and the insulating electron glass of semiconductors. Prospects for the realization of such glassy phases in cold-atom systems are discussed.

Recent studies of strongly interacting atoms and photons in optical cavities have rekindled interest in the Dicke model of atomic qubits coupled to discrete photon cavity modes. We study the multimode Dicke model with variable atom-photon couplings. We argue that a quantum spin-glass phase can appear, with a random linear combination of the cavity modes superradiant. We compute atomic and photon spectral response functions across this quantum phase transition, both of which should be accessible in experiments.

In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter and could evolve into a “cavity glass microscope” for frustrated quantum systems out of equilibrium. Here we develop the nonequilibrium theory of the multimode Dicke model with quenched disorder and Markovian dissipation. Using a unified Keldysh path integral approach, we show that the defining features of a low-temperature glass, representing a critical phase of matter with algebraically decaying temporal correlation functions, are seen to be robust against the presence of dissipation due to cavity loss. The universality class, however, is modified due to the Markovian bath. The presence of strong disorder leads to an enhanced equilibration of atomic and photonic degrees of freedom, including the emergence of a common low-frequency effective temperature. The imprint of the atomic spin-glass physics onto the photon subsystem realizes a “photon glass” state and makes it possible to detect the glass state by standard experimental techniques of quantum optics. We provide an unambiguous characterization of the superradiant and glassy phases in terms of fluorescence spectroscopy, homodyne detection, and the temporal photon correlation function g(2)(τ).

We show that the Néel states of two-dimensional antiferromagnets have low energy vector boson excitations in the vicinity of deconfined quantum critical points. We compute the universal damping of these excitations arising from spin-wave emission. Detection of such a vector boson will demonstrate the existence of emergent topological gauge excitations in a quantum spin system.

We investigate non-equilibrium phase transitions for driven atomic ensembles, interacting with a cavity mode, coupled to a Markovian dissipative bath. In the thermodynamic limit and at low-frequencies, we show that the distribution function of the photonic mode is thermal, with an e↵ective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated su- perradiance transition. Motivated by these considerations, we develop a general Keldysh path integral approach, that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number of atoms N. For finite N, the photon mode behaves as a damped, classical non-linear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any N and correctly captures the atoms’ depolarization due to dissipative dephasing.

We compute three-point correlators between the stress-energy tensor and the conserved currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then perform the computation using holography. In the holographic approach, the correlators are computed from an effective action on (3+1)-dimensional anti-de Sitter space (AdS4) and depend upon the coefficient γ of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus, fixing the values of γ. The CFTs of free fermions and bosons take the values γ=1/12,−1/12, respectively, and so saturate the bound ∣∣γ∣∣≤1/12 obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of γ. The value of γ also controls the frequency dependence of the conductivity and other properties of quantum critical transport at nonzero temperatures. Our results for the values of γ lead to an appealing physical interpretation of particlelike or vortexlike transport near quantum phase transitions of interest in condensed-matter physics. This paper includes Appendices reviewing key features of the AdS-CFT correspondence for condensed-matter physicists.

We compute current correlators of the CPN−1 field theory in 2+1 dimensions, both at the critical point and in the phase with spontaneously broken SU(N) symmetry. Universal constants are obtained to next-to-leading order in the 1/N expansion. Implications are noted for quantum critical points of antiferromagnets and their vicinity.

The hyperscaling property implies that spatially isotropic critical quantum states in d spatial dimensions have a specific heat which scales with temperature as Td/z, and an optical conductivity which scales with frequency as ω(d−2)/z for ω ≫ T, where z is the dynamic critical exponent. We examine the spin-density wave critical fixed point of metals in d = 2 found by Sur and Lee (Phys. Rev. B 91, 125136 (2015)) in an expansion in ϵ = 3 − d. We find that the contributions of the “hot spots” on the Fermi surface to the optical conductivity and specific heat obey hyperscaling (up to logarithms), and agree with the results of the large N analysis of the optical conductivity by Hartnoll et al. (Phys. Rev. 84, 125115 (2011)). With a small bare velocity of the boson associated with the spin density wave order, there is an intermediate energy regime where hyperscaling is violated with d → dt, where dt = 1 is the number of dimensions transverse to the Fermi surface. We also present a Boltzmann equation analysis which indicates that the hot spot contribution to the DC conductivity has the same scaling as the optical conductivity, with T replacing ω.