arXiv subjects

Aidan Zabalo

Publications and source records attributed to Aidan Zabalo.

9 recordsLinked to original sources

arXiv2024

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. Our numerical estimation of the critical properties of the entanglement transition at finite system sizes appears distinct from the generic non-conserving case and percolation. We provide two possible interpretations of this observation: (a) these two transitions occur at different measurement rates in the thermodynamic limit, but at finite system sizes their critical fans overlap and the critical exponents we probed here show a combination of both the criticality. 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. (b) these two transitions occur at the same measurement rate at any length scale. Within this interpretation, our estimation of all the critical exponents are sharply different than the non-conserving case, again confirming the presence of a new universality class due 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 finite-size system will see anomalously large exponents predicted by our numerical analysis.

cond-mat.dis-nn↗

arXiv2024

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 $β$ to exceed the Luck bound $ν\ge 1/(1-β)$ for the stability of the MIPT, where $ν=1.28(2)$. Via robust 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, $β$. 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 $ψ\cong β$, finding excellent agreement with the conclusions of real space renormalization group calculations.

cond-mat.dis-nn↗

arXiv2022

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 Rényi entropies grow sub-ballistically as $\sqrt{t}$ in the absence of measurement, for even an infinitesimal rate of measurements, all average Rényi entropies grow ballistically with time $\sim t$. 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.

cond-mat.dis-nn↗

arXiv2022

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.

cond-mat.supr-con↗

arXiv2022

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 $\ell$ scales as $S \sim \sqrt{\ell}$; moreover, the dynamical critical exponent $z = \infty$. 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.

cond-mat.dis-nn↗

arXiv2022

Operator scaling dimensions and multifractality at measurement-induced transitions

Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large onsite Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

cond-mat.dis-nn↗

arXiv2021

Time reversal symmetry protected chaotic fixed point in the quench dynamics of a topological $p$-wave superfluid

We study the quench dynamics of a topological $p$-wave superfluid with two competing order parameters, $Δ_\pm(t)$. When the system is prepared in the $p+ip$ ground state and the interaction strength is quenched, only $Δ_+(t)$ is nonzero. However, we show that fluctuations in the initial conditions result in the growth of $Δ_-(t)$ and chaotic oscillations of both order parameters. We term this behavior phase III'. In addition, there are two other types of late time dynamics -- phase I where both order parameters decay to zero and phase II where $Δ_+(t)$ asymptotes to a nonzero constant while $Δ_-(t)$ oscillates near zero. Although the model is nonintegrable, we are able to map out the exact phase boundaries in parameter space. Interestingly, we find phase III' is unstable with respect to breaking the time reversal symmetry of the interaction. When one of the order parameters is favored in the Hamiltonian, the other one rapidly vanishes and the previously chaotic phase III' is replaced by the Floquet topological phase III that is seen in the integrable chiral $p$-wave model.

cond-mat.supr-con↗

arXiv2021

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 $s$-wave and topological $p_x+ip_y$ 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.

cond-mat.quant-gas↗

arXiv2020

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 $1+1$ dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate $p_c = 0.17(1)$. 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 $S_n$ depends strongly on the Rényi index $n$; 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.

cond-mat.dis-nn↗