Phases and phase transitions in quantum circuits

Understanding the dynamics of quantum information on circuits consisting of unitary gates and local measurements applied to the quantum state is important for realizing quantum computers. Recently it was shown that the state evolved by such a circuit can undergo a transition from a volume law entanglement entropy to an area law when the measurement rate exceeds a critical value.

In paper [1] we explained the transition as a change in the quantum encoding power of the circuit. The unitary gates naturally encode quantum information non-locally, thus hiding and protecting it from the deleterious effect of local measurements, as long as those are sufficiently rare. The volume law phase is where the circuit behaves as a quantum error correcting code able to coherently propagate a finite density of logical qubits. In paper [2] we formulated a mapping of the ensemble of quantum trajectories evolving in the circuit to a classical statistical mechanics model, allowing to analyze the phase transition and identify new signatures of the transition that directly .

In the most recent paper [3] we show that a much richer phase structure emerges if symmetries are imposed on the quantum circuit. The classification into phases is governed by an enlarged effective symmetry, which combines the physical circuit symmetry with dynamical symmetries associated with the ensemble of quantum trajectories. This leads to phases that would not be possible as equilibrium states. Two examples we give are: (i) a 1+1 dimensional circuit with Z2 spin symmetry gives rise to a number of phases including volume law states with distinct broken symmetries; (ii) A circuit with Gaussian fermion gates obeying only Z2 fermion parity symmetry, nonetheless exhibits a broad critical phase separated from area law phases by a measurement induced Kosterlitz-Thouless transition.

Fast scramblers

The SYK model is a solvable model of interacting fermions; it realizes an interesting low temperature non fermi liquid phase that can be shown to be dual to a black hole in AdS₂ . Like a black hole it is a "fast scrambler" of information, saturating a proven quantum bound on chaos. But the SYK model can only be a caricature of real critical fermion systems because it is devoid of any spatial structure. Extending the system to a lattice of coupled SYK "dots" doesn't quite work as it leads to unphysical local critical behavior. In paper [1] we solve this problem by introducing a modified Gross-Neveu-Yukawa field theory with a large number of fermion and boson flavors. We obtain Lorentz invariant critical solutions and demonstrate fast scrambling in one spatial dimension. More broadly this model suggests a new large N scheme for capturing strongly coupled critical points in fermion systems.

The higher dimensional extension relied on our earlier work on the properties of "low rank" SYK models in zero dimensions (papers [2] and [3]). The low rank refers to the interaction matrix which has rank of order N (number of fermions) rather than the unphysical rank N². In addition we showed that SYK models with rank N can be tuned between different phases including fast scramblers, Fermi liquids and marginal Fermi liquids.

Unconventional quantum critical points
and strange metals

Analytis' group has recently observed evidence for an unconventional quantum phase transition in the material CeCoIn5 involving a change of the Fermi surface volume without any sign of symmetry breaking (paper [1]). The transition, which cannot be described by the standard Landau framework, is accompanied by anomalous transport properties including linear in temperature resistivity and a strong enhancement of the Hall coefficient. We collaborated with Analytis' group and explained the behavior of the Hall coefficient within a phenomenological theory of a transition between a normal metal and an exotic metal with fractionalized excitations.

Later, in paper [2] we developed a microscopic theory of this transition which captures the strange metal behavior within a new solvable large N limit. The theory naturally predicts resistivity that grows linearly with temperature at the critical point with a nearly universal slope, indicating so called "Planckian transport".

Critical behavior near the many-body localization transition in driven open systems

Many-body localized systems fail to thermalize as isolated systems, but do thermalize when coupled to an external bath. For this reason true MBL is not expected to occur in solids, which are always coupled to a phonon bath. Nonetheless, we argue that if such a system is driven out of equilibrium (e.g. by coupling it to an additional bath at a different temperature or illuminating it), then sharp universal signatures of MBL and the critical behavior associated with the MBL transition, emerge in the limit where both the coupling to the bath and the drive are weak. Under these conditions, a thermalizing system establishes a Gibbs state with a uniform temperature, while an MBL system develops a generalized Gibbs state with non uniform temperature. The latter is a vestige of local conservation of energy in the closed MBL system. Thus the temperature variance can serve as an order parameter for a transition, which becomes sharp in the limit of vanishing dissipative couplings.

In a second paper we show how the critical behavior manifests in the singular dependence of the energy variance on the dissipative coupling (epsilon in the figures). These insights may open the door to systematic studies of MBL in solids. In addition, we utilize these ideas to develop a numerical matrix-product operator approach that overcomes certain limitations of exact diagonalization studies of the MBL critical point.

A universal operator growth hypothesis

Universal dynamics in boundary driven conformal field theories

Integrable and chaotic dynamics of spins coupled to an optical cavity