8 research outputs found
Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids
Non-analyticities in the logarithm of the Loschmidt echo, known as dynamical
quantum phase transitions [DQPTs], are a recently introduced attempt to
classify the myriad of possible phenomena which can occur in far from
equilibrium closed quantum systems. In this work, we analytically investigate
the Loschmidt echo in nonequilibrium -wave and topological
fermionic superfluids. We find that the presence of non-analyticities in the
echo is not invariant under global rotations of the superfluid phase. We remedy
this deficiency by introducing a more general notion of a grand canonical
Loschmidt echo. Overall, our study shows that DQPTs are not a good indicator
for the long time dynamics of an interacting system. In particular, there are
no DQPTs to tell apart distinct dynamical phases of quenched BCS
superconductors. Nevertheless, they can signal a quench induced change in the
topology and also keep track of solitons emerging from unstable stationary
states of a BCS superconductor.Comment: 24 pages, 12 figure
Nonlocality as the source of purely quantum dynamics of BCS superconductors
We show that the classical (mean-field) description of far from equilibrium
superconductivity is exact in the thermodynamic limit for local observables but
breaks down for global quantities, such as the entanglement entropy or
Loschmidt echo. We do this by solving for and comparing exact quantum and exact
classical long-time dynamics of a BCS superconductor with interaction strength
inversely proportional to time and evaluating local observables explicitly.
Mean field is exact for both normal and anomalous averages (superconducting
order) in the thermodynamic limit. However, for anomalous expectation values,
this limit does not commute with adiabatic and strong coupling limits and, as a
consequence, their quantum fluctuations can be unusually strong. The long-time
steady state of the system is a gapless superconductor whose superfluid
properties are only accessible through energy resolved measurements. This state
is nonthermal but conforms to an emergent generalized Gibbs ensemble. Our study
clarifies the nature of symmetry-broken many-body states in and out of
equilibrium and fills a crucial gap in the theory of time-dependent quantum
integrability.Comment: 30 pages, 10 figures, new titl
Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits
We study critical properties of the entanglement and charge-sharpening
measurement-induced phase transitions in a non-unitary quantum circuit evolving
with a U(1) conserved charge. Many critical properties appear distinct from the
generic non-conserving case and percolation; however, upon interpreting the
critical features as mixtures of both entanglement and charge-sharpening
transitions, many critical features are brought within range of the generic
case. Nonetheless, the multifractal properties of the entanglement transition
remain distinct from the generic case without any symmetry, indicating a unique
universality class due to the U(1) symmetry. We compute entanglement critical
exponents and correlation functions via various ancilla measures, use a
transfer matrix for multifractality, and compute correlators associated with
charge sharpening to explain these findings. Through these correlators, we also
find evidence consistent with the charge-sharpening transition being of the
Berezinskii-Kosterlitz-Thouless type (including the predicted "jump" in
stiffness), which simultaneously argues for a broad critical fan for this
transition. As a result, attempts to measure critical properties in this system
will see anomalously large exponents consistent with overlapping criticality.Comment: 12+5 pages, 8+6 figure
Measurement induced criticality in quasiperiodic modulated random hybrid circuits
We study one-dimensional hybrid quantum circuits perturbed by quenched
quasiperiodic (QP) modulations across the measurement-induced phase transition
(MIPT). Considering non-Pisot QP structures, characterized by unbounded
fluctuations, allows us to tune the wandering exponent to exceed the
Luck bound for the stability of the MIPT where . Via large-scale numerical simulations of random Clifford circuits
interleaved with local projective measurements, we find that sufficiently large
QP structural fluctuations destabilize the MIPT and induce a flow to a broad
family of critical dynamical phase transitions of the infinite QP type that is
governed by the wandering exponent, . We numerically determine the
associated critical properties, including the correlation length exponent
consistent with saturating the Luck bound, and a universal activated dynamical
scaling with activation exponent , finding excellent
agreement with the conclusions of real space renormalization group
calculations.Comment: 14 pages, 13 figure
Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
Monitored quantum circuits can exhibit an entanglement transition as a
function of the rate of measurements, stemming from the competition between
scrambling unitary dynamics and disentangling projective measurements. We study
how entanglement dynamics in non-unitary quantum circuits can be enriched in
the presence of charge conservation, using a combination of exact numerics and
a mapping onto a statistical mechanics model of constrained hard-core random
walkers. We uncover a charge-sharpening transition that separates different
scrambling phases with volume-law scaling of entanglement, distinguished by
whether measurements can efficiently reveal the total charge of the system. We
find that while R\'enyi entropies grow sub-ballistically as in the
absence of measurement, for even an infinitesimal rate of measurements, all
average R\'enyi entropies grow ballistically with time . We study
numerically the critical behavior of the charge-sharpening and entanglement
transitions in U(1) circuits, and show that they exhibit emergent Lorentz
invariance and can also be diagnosed using scalable local ancilla probes. Our
statistical mechanical mapping technique readily generalizes to arbitrary
Abelian groups, and offers a general framework for studying
dissipatively-stabilized symmetry-breaking and topological orders.Comment: 28 pages, 17 figure
Critical properties of the measurement-induced transition in random quantum circuits
We numerically study the measurement-driven quantum phase transition of
Haar-random quantum circuits in dimensions. By analyzing the tripartite
mutual information we are able to make a precise estimate of the critical
measurement rate . We extract estimates for the associated bulk
critical exponents that are consistent with the values for percolation, as well
as those for stabilizer circuits, but differ from previous estimates for the
Haar-random case. Our estimates of the surface order parameter exponent appear
different from that for stabilizer circuits or percolation, but we are unable
to definitively rule out the scenario where all exponents in the three cases
match. Moreover, in the Haar case the prefactor for the entanglement entropies
depends strongly on the R\'enyi index ; for stabilizer circuits and
percolation this dependence is absent. Results on stabilizer circuits are used
to guide our study and identify measures with weak finite-size effects. We
discuss how our numerical estimates constrain theories of the transition.Comment: 6 pages + Supplemental materials (Updated with published version
Infinite-randomness criticality in monitored quantum dynamics with static disorder
We consider a model of monitored quantum dynamics with quenched spatial
randomness: specifically, random quantum circuits with spatially varying
measurement rates. These circuits undergo a measurement-induced phase
transition (MIPT) in their entanglement structure, but the nature of the
critical point differs drastically from the case with constant measurement
rate. In particular, at the critical measurement rate, we find that the
entanglement of a subsystem of size scales as ;
moreover, the dynamical critical exponent . The MIPT is flanked by
Griffiths phases with continuously varying dynamical exponents. We argue for
this infinite-randomness scenario on general grounds and present numerical
evidence that it captures some features of the universal critical properties of
MIPT using large-scale simulations of Clifford circuits. These findings
demonstrate that the relevance and irrelevance of perturbations to the MIPT can
naturally be interpreted using a powerful heuristic known as the Harris
criterion.Comment: (7 + 7) pages, (3 + 5) figures, (0 + 1) table