arXiv subjects

Ehud Altman

Publications and source records attributed to Ehud Altman.

At least 37 records · Page 2Linked to original sources

arXiv2023

Probing post-measurement entanglement without post-selection

We study the problem of observing quantum collective phenomena emerging from large numbers of measurements. These phenomena are difficult to observe in conventional experiments because, in order to distinguish the effects of measurement from dephasing, it is necessary to post-select on sets of measurement outcomes whose Born probabilities are exponentially small in the number of measurements performed. An unconventional approach, which avoids this exponential `post-selection problem', is to construct cross-correlations between experimental data and the results of simulations on classical computers. However, these cross-correlations generally have no definite relation to physical quantities. We first show how to incorporate shadow tomography into this framework, thereby allowing for the construction of quantum information-theoretic cross-correlations. We then identify cross-correlations which both upper and lower bound the measurement-averaged von Neumann entanglement entropy, and additional cross-correlations which lower bound the measurement-averaged purity and entanglement negativity. These bounds show that experiments can be performed to constrain post-measurement entanglement without the need for post-selection. To illustrate our technique we consider how it could be used to observe the measurement-induced entanglement transition in Haar-random quantum circuits. We use exact numerical calculations as proxies for quantum simulations and, to highlight the fundamental limitations of classical memory, we construct cross-correlations with tensor-network calculations at finite bond dimension. Our results reveal a signature of measurement-induced criticality that can be observed using a quantum simulator in polynomial time and with polynomial classical memory.

quant-ph↗

arXiv2023

Fractonic Luttinger Liquids and Supersolids in a Constrained Bose-Hubbard Model

Quantum many-body systems with fracton constraints are widely conjectured to exhibit unconventional low-energy phases of matter. In this work, we demonstrate the existence of a variety of such exotic quantum phases in the ground states of a dipole-moment conserving Bose-Hubbard model in one dimension. For integer boson fillings, we perform a mapping of the system to a model of microscopic local dipoles, which are composites of fractons. We apply a combination of low-energy field theory and large-scale tensor network simulations to demonstrate the emergence of a dipole Luttinger liquid phase. At non-integer fillings our numerical approach shows an intriguing compressible state described by a quantum Lifshitz model in which charge density-wave order coexists with dipole long-range order and superfluidity - a `dipole supersolid'. While this supersolid state may eventually be unstable against lattice effects in the thermodynamic limit, its numerical robustness is remarkable. We discuss potential experimental implications of our results.

cond-mat.quant-gas↗

arXiv2023

Nonlocality and entanglement in measured critical quantum Ising chains

We study the effects of measurements, performed with a finite density in space, on the ground state of the one-dimensional transverse-field Ising model at criticality. Local degrees of freedom in critical states exhibit long-range entanglement, and as a result, local measurements can have highly nonlocal effects. Our analytical investigation of correlations and entanglement in the ensemble of measured states is based on properties of the Ising conformal field theory (CFT), where measurements appear as (1+0)-dimensional defects in the (1+1)-dimensional Euclidean spacetime. So that we can verify our predictions using large-scale free-fermion numerics, we restrict ourselves to parity-symmetric measurements. To describe their averaged effects analytically we use a replica approach, and we show that the defect arising in the replica theory is an irrelevant perturbation to the Ising CFT. Strikingly, the asymptotic scalings of averaged correlations and entanglement entropy are therefore unchanged relative to the ground state. In contrast, the defect generated by postselecting on the most likely measurement outcomes is exactly marginal. We then find that the exponent governing postmeasurement order parameter correlations, as well as the ''effective central charge'' governing the scaling of entanglement entropy, vary continuously with the density of measurements in space. Our work establishes new connections between the effects of measurements on many-body quantum states and of physical defects on low-energy equilibrium properties.

cond-mat.stat-mech↗

arXiv2023

Cross Entropy Benchmark for Measurement-Induced Phase Transitions

We investigate the prospects of employing the linear cross-entropy to experimentally access measurement-induced phase transitions (MIPT) without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with different initial states, the linear cross-entropy $χ$ between the bulk measurement outcome distributions in the two circuits acts as a boundary order parameter, and can be used to distinguish the volume law from area law phases. In the volume law phase (and in the thermodynamic limit) the bulk measurements cannot distinguish between the two different initial states, and $χ= 1$. In the area law phase $χ< 1$. For circuits with Clifford gates, we provide numerical evidence that $χ$ can be sampled to accuracy $ε$ from $O(1/ε^2)$ trajectories, by running the first circuit on a quantum simulator without postselection, aided by a classical simulation of the second. We also find that for weak depolarizing noise the signature of the MIPT is still present for intermediate system sizes. In our protocol we have the freedom of choosing initial states such that the "classical" side can be simulated efficiently, while simulating the "quantum" side is still classically hard.

quant-ph↗

arXiv2023

A universal crossover in quantum circuits governed by a proximate classical error correction transition

We formulate a semi-classical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements. As a starting point we define a random circuit model with nearest neighbor classical gates interrupted by erasure errors. In analogy with the quantum setting, this system undergoes a purification transition at a critical error rate above which the classical information entropy in the output state vanishes. We show that this phase transition is in the directed percolation universality class, consistent with the fact that having zero entropy is an absorbing state of the dynamics; this classical circuit cannot generate entropy. Adding an arbitrarily small density of quantum gates in the presence of errors eliminates the transition by destroying the absorbing state: the quantum gates generate internal entanglement, which can be effectively converted to classical entropy by the errors. We describe the universal properties of this instability in an effective model of the semi-classical circuit. Our model highlights the crucial differences between information dynamics in classical and quantum circuits.

quant-ph↗

arXiv2022

Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit

Generic many-body systems coupled to an environment lose their quantum entanglement due to decoherence and evolve to a mixed state with only classical correlations. Here, we show that measurements can stabilize quantum entanglement within open quantum systems. Specifically, in random unitary circuits with dephasing at the boundary, we find both numerically and analytically that projective measurements performed at a small nonvanishing rate results in a steady state with an $L^{1/3}$ power-law scaling entanglement negativity within the system. Using an analytical mapping to a statistical mechanics model of directed polymers in a random environment, we show that the power-law negativity scaling can be understood as Kardar-Parisi-Zhang fluctuations due to the random measurement locations. Further increasing the measurement rate leads to a phase transition into an area-law negativity phase, which is of the same universality as the entanglement transition in monitored random circuits without decoherence.

quant-ph↗

arXiv2022

Magnetic memory and spontaneous vortices in a van der Waals superconductor

Doped Mott insulators exhibit some of the most intriguing quantum phases of matter, including quantum spin-liquids, unconventional superconductors, and non-Fermi liquid metals. Such phases often arise when itinerant electrons are close to a Mott insulating state, and thus experience strong spatial correlations. Proximity between different layers of van der Waals heterostructures naturally realizes a platform for experimentally studying the relationship between localized, correlated electrons and itinerant electrons. Here, we explore this relationship by studying the magnetic landscape of 4Hb-TaS2, which realizes an alternate stack of a candidate spin liquid and a superconductor. We report on a spontaneous vortex phase whose vortex density can be trained in the normal state. We show that time reversal symmetry is broken above Tc, indicating the presence of a magnetic phase independent of the superconductor. Strikingly, this phase does not generate detectable magnetic signals. We use scanning superconducting quantum interference device (SQUID) microscopy to show that it is incompatible with ferromagnetic ordering. The discovery of this new form of hidden magnetism illustrates how combining superconductivity with a strongly correlated system can lead to new, unexpected physics.

cond-mat.supr-con↗

arXiv2022

Solvable Theory of a Strange Metal at the Breakdown of a Heavy Fermi Liquid

We introduce an effective theory for quantum critical points (QCPs) in heavy fermion systems, involving a change in carrier density without symmetry breaking. Our new theory captures a strongly coupled metallic QCP, leading to robust marginal Fermi liquid transport phenomenology, and associated linear in temperature ($T$) "strange metal" resistivity, all within a controlled large $N$ limit. In the parameter regime of strong damping of emergent bosonic excitations, the QCP also displays a near-universal "Planckian" transport lifetime, $τ_{\mathrm{tr}}\sim\hbar/(k_BT)$. This is contrasted with the conventional so-called "slave boson" theory of the Kondo breakdown, where the large $N$ limit describes a weak coupling fixed point and non-trivial transport behavior may only be obtained through uncontrolled $1/N$ corrections. We also compute the weak-field Hall coefficient within the effective model as the system is tuned across the transition. We further find that between the two plateaus, reflecting the different carrier densities in the two Fermi liquid phases, the Hall coefficient can develop a peak in the critical crossover regime, like in recent experimental findings, in the parameter regime of weak boson damping.

cond-mat.str-el↗

arXiv2022

Absence of heating in a uniform Fermi gas created by periodic driving

Ultracold atomic gas provides a useful tool to explore many-body physics. One of the recent additions to this experimental toolbox is the Floquet engineering, where periodic modulation of the Hamiltonian allows the creation of effective potentials that do not exist otherwise. When subject to external modulations, however, generic interacting many-body systems absorb energy, thus posing a heating problem that may impair the usefulness of this method. For discrete systems with bounded local energy, an exponentially suppressed heating rate with the driving frequency has been observed previously, leaving the system in a prethermal state for exceedingly long durations. But for systems in continuous space, the situation remains unclear. Here we show that Floquet engineering can be employed to a strongly interacting degenerate Fermi gas held in a flat box-like potential without inducing excessive heating on experimentally relevant timescales. The driving eliminates the effect of a spin-dependent potential originating from a simultaneous magnetic levitation of two different spin states. We calculate the heating rate and obtain a power-law suppression with the drive frequency. To further test the many-body behavior of the driven gas, we measure both the pair-condensation fraction at unitarity and the contact parameter across the BEC-BCS crossover. At low driving frequencies, the condensate fraction is reduced by the time-dependent force, but at higher frequencies, it revives and attains an even higher value than without driving. Our results are promising for future exploration of exotic many-body phases of a bulk strongly-interacting Fermi gas with dynamically engineered Hamiltonians.

cond-mat.quant-gas↗

arXiv2021

Symmetry enriched phases of quantum circuits

Quantum circuits consisting of random unitary gates and subject to local measurements have been shown to undergo a phase transition, tuned by the rate of measurement, from a state with volume-law entanglement to an area-law state. From a broader perspective, these circuits generate a novel ensemble of quantum many-body states at their output. In this paper, we characterize this ensemble and classify the phases that can be established as steady states. Symmetry plays a nonstandard role in that the physical symmetry imposed on the circuit elements does not on its own dictate the possible phases. Instead, it is extended by dynamical symmetries associated with this ensemble to form an enlarged symmetry. Thus, we predict phases that have no equilibrium counterpart and could not have been supported by the physical circuit symmetry alone. We give the following examples. First, we classify the phases of a circuit operating on qubit chains with $\mathbb{Z}_2$ symmetry. One striking prediction, corroborated with numerical simulation, is the existence of distinct volume-law phases in one dimension, which nonetheless support true long-range order. We furthermore argue that owing to the enlarged symmetry, this system can in principle support a topological area-law phase, protected by the combination of the circuit symmetry and a dynamical permutation symmetry. Second, we consider a Gaussian fermionic circuit that only conserves fermion parity. Here the enlarged symmetry gives rise to a $U(1)$ critical phase at moderate measurement rates and a Kosterlitz-Thouless transition to area-law phases. We comment on the interpretation of the different phases in terms of the capacity to encode quantum information. We discuss close analogies to the theory of spin glasses pioneered by Edwards and Anderson as well as crucial differences that stem from the quantum nature of the circuit ensemble.

cond-mat.stat-mech↗

arXiv2021

The Measurement-induced Transition in Long-range Interacting Quantum Circuits

The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of long-range, power-law interactions. For sufficiently weak power-laws, the measurement-induced transition is described by conformal field theory, analogous to short-range-interacting hybrid circuits. However, beyond a critical power-law, we demonstrate that long-range interactions give rise to a continuum of non-conformal universality classes, with continuously varying critical exponents. We numerically determine the phase diagram for a one-dimensional, long-range-interacting hybrid circuit model as a function of the power-law exponent and the measurement rate. Finally, by using an analytic mapping to a long-range quantum Ising model, we provide a theoretical understanding for the critical power-law.

quant-ph↗

arXiv2021

Dirac Fast Scramblers

We introduce a family of Gross-Neveu-Yukawa models with a large number of fermion and boson flavors as higher dimensional generalizations of the Sachdev-Ye-Kitaev model. The models may be derived from local lattice couplings and give rise to Lorentz invariant critical solutions in 1+1 and 2+1 dimensions. These solutions imply anomalous dimensions of both bosons and fermions tuned by the number ratio of boson to fermion flavors. In 1+1 dimension the solution represents a stable critical phase, while in 2+1 dimension it governs a quantum phase transition. We compute the out of time order correlators in the 1+1 dimensional model, showing that it exhibits growth with the maximal Lyapunov exponent $λ_L=2πT$ in the low temperature limit.

cond-mat.str-el↗

arXiv2020

Evidence for freezing of charge degrees of freedom across a critical point in CeCoIn$_5$

The presence of a quantum critical point separating two distinct zero-temperature phases is thought to underlie the `strange' metal state of many high-temperature superconductors. The nature of this quantum critical point, as well as a description of the resulting strange metal, are central open problems in condensed matter physics. In large part, the controversy stems from the lack of a clear broken symmetry to characterize the critical phase transition, and this challenge is no clearer than in the example of the unconventional superconductor CeCoIn$_5$. Through Hall effect and Fermi surface measurements of CeCoIn$_5$, in comparison to ab initio calculations, we find evidence for a critical point that connects two Fermi surfaces with different volumes without apparent symmetry-breaking, indicating the presence of a transition that involves an abrupt localization of one sector of the charge degrees of freedom. We present a model for the anomalous electrical Hall resistivity of this material based on the conductivity of valence charge fluctuations.

cond-mat.str-el↗

arXiv2020

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

Coupling a many-body localized system to a thermal bath breaks local conservation laws and washes out signatures of localization. When the bath is non-thermal or when the system is also weakly driven, local conserved quantities acquire a highly non-thermal stationary value. We demonstrate how this property can be used to study the many-body localization phase transition in weakly open systems. Here, the strength of the coupling to the non-thermal baths plays a similar role as a finite temperature in a $T=0$ quantum phase transition. By tuning this parameter, we can detect key features of the MBL transition: the divergence of the dynamical exponent due to Griffiths effects in one dimension and the critical disorder strength. We apply these ideas to study the MBL critical point numerically. The possibility to observe critical signatures of the MBL transition in an open system allows for new numerical approaches that overcome the limitations of exact diagonalization studies. Here we propose a scalable numerical scheme to study the MBL critical point using matrix-product operator solution to the Lindblad equation.

cond-mat.str-el↗

arXiv2020

Scrambling versus relaxation in Fermi and non-Fermi liquids

We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids to fast scramblers. The analytic calculation, controlled by a small coupling constant and large $N$, allows us to clarify the relations between the quasi-particle relaxation rate $1/τ$ and the Lyapunov exponent $λ_L$ characterizing scrambling. In the Fermi liquid states we find that the quasi-particle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/τ\gg T$, we find that $λ_L$ is always $T$-linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. $λ_L$ approaches the general upper bound $2πT$ at the transition to a fast scrambling state. Finally in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a non analytic function $\sim g \ln (1/g)$ of the coupling constant $g$.

cond-mat.str-el↗

arXiv2020

Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition

We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by the volume-law and area-law scaling entanglement entropy in steady states. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling. We confirm these results using numerical simulations and obtain the phase diagram of our model. Our work shows that information scrambling plays a crucial role in understanding the dynamics of entanglement in an open quantum system and relates the entanglement phase transition to changes in quantum channel capacity.

quant-ph↗

arXiv2020

Theory of the phase transition in random unitary circuits with measurements

We present a theory of the entanglement transition tuned by measurement strength in qudit chains evolved by random unitary circuits and subject to either weak or random projective measurements. The transition can be understood as a nonanalytic change in the amount of information extracted by the measurements about the initial state of the system, quantified by the Fisher information. To compute the von~Neumann entanglement entropy $S$ and the Fisher information $\mathcal{F}$, we apply a replica method based on a sequence of quantities $\tilde{S}^{(n)}$ and $\mathcal{F}^{(n)}$ that depend on the $n$-th moments of density matrices and reduce to $S$ and $\mathcal{F}$ in the limit $n\to 1$. These quantities with $n\ge 2$ are mapped to free energies of a classical spin model with $n!$ internal states in two dimensions with specific boundary conditions. In particular, $\tilde{S}^{(n)}$ is the excess free energy of a domain wall terminating on the top boundary, and $\mathcal{F}^{(n)}$ is related to the magnetization on the bottom boundary. Phase transitions occur as the spin models undergo ordering transitions in the bulk. Taking the limit of large local Hilbert space dimension $q$ followed by the replica limit $n\to 1$, we obtain the critical measurement probability $p_c=1/2$ and identify the transition as a bond percolation in the 2D square lattice in this limit. Finally, we show there is no phase transition if the measurements are allowed in an arbitrary nonlocal basis, thereby highlighting the relation between the phase transition and information scrambling. We establish an explicit connection between the entanglement phase transition and the purification dynamics of a mixed state evolution and discuss implications of our results to experimental observations of the transition and simulability of quantum dynamics.

cond-mat.stat-mech↗

arXiv2020

Low-rank Sachdev-Ye-Kitaev models

Motivated by recent works on atom-cavity realizations of fast scramblers, and on Cooper pairing in non-Fermi liquids, we study a family of solvable variants of the ($q=4$) Sachdev-Ye-Kitaev model in which the rank and eigenvalue distribution of the coupling matrix $J_{ij,kl}$ are tuneable. When the rank is proportional to the number of fermions, the low temperature behavior is sensitive to the eigenvalue distribution. We obtain a complete classification of the possible non-Fermi liquid quantum phases. These include two previously studied phases whose fermion scaling dimension depends continuously on the rank; we show that they are maximally chaotic, but necessitate {an extensively degenerate or negative semidefinite coupling matrix}. More generic distributions give rise to "almost Fermi liquids" with a scaling dimension $Δ= 1/2$, but which differ from a genuine Fermi-liquid in quasi-particle decay rate, quantum Lyapunov exponent and/or specific heat.

cond-mat.str-el↗