arXiv subjects

Jad C. Halimeh

Publications and source records attributed to Jad C. Halimeh.

At least 127 records · Page 7Linked to original sources

arXiv2020

Staircase Prethermalization and Constrained Dynamics in Lattice Gauge Theories

The dynamics of lattice gauge theories is characterized by an abundance of local symmetry constraints. Although errors that break gauge symmetry appear naturally in NISQ-era quantum simulators, their influence on the gauge-theory dynamics is insufficiently investigated. As we show, a small gauge breaking of strength $λ$ induces a staircase of long-lived prethermal plateaus. The number of prethermal plateaus increases with the number of matter fields $L$, with the last plateau being reached at a timescale $λ^{-L/2}$, showing an intimate relation of the concomitant slowing down of dynamics with the number of local gauge constraints. Our results bode well for NISQ quantum devices, as they indicate that the proliferation timescale of gauge-invariance violation is counterintuitively delayed exponentially in system size.

cond-mat.quant-gas↗

arXiv2020

Origin of staircase prethermalization in lattice gauge theories

Quantum many-body systems with exact local gauge symmetries exhibit rich out-of-equilibrium physics such as constrained dynamics and disorder-free localization. In a joint submission [J. C. Halimeh and P. Hauke, arXiv:2004.07248], we present evidence of \textit{staircase prethermalization} in a $\mathrm{Z}_2$ lattice gauge theory subjected to a small breaking of gauge invariance. Here, we consolidate this finding and the associated emergent nonperturbative timescales analytically and numerically. By means of a Magnus expansion, we demonstrate how exact resonances between different gauge-invariant supersectors are the main reason behind the emergence of staircase prethermalization. Furthermore, we showcase the robustness of our conclusions against various initial conditions including different system sizes, matter fillings, and gauge-invariance sectors, in addition to various boundary conditions, such as different maximal on-site matter occupations. We also elaborate on how our conclusions are unique to local-symmetry models and why they break down in the case of global-symmetry breaking. We moreover extend our results to $\mathrm{U}(1)$ lattice gauge theories, illustrating the generality of our findings. Our work offers an analytic footing into the constrained dynamics of lattice gauge theories and provides proof of a certain intrinsic robustness of gauge-theory dynamics to errors in experimental settings.

cond-mat.str-el↗

arXiv2020

Quasiparticle origin of dynamical quantum phase transitions

Considering nonintegrable quantum Ising chains with exponentially decaying interactions, we present matrix product state results that establish a connection between low-energy quasiparticle excitations and the kind of nonanalyticities in the Loschmidt return rate. When domain walls in the spectrum of the quench Hamiltonian are energetically favored to be bound rather than freely propagating, anomalous cusps appear in the return rate regardless of the initial state. In the nearest-neighbor limit, domain walls are always freely propagating, and anomalous cusps never appear. As a consequence, our work illustrates that models in the same equilibrium universality class can still exhibit fundamentally distinct out-of-equilibrium criticality. Our results are accessible to current ultracold-atom and ion-trap experiments.

cond-mat.str-el↗

arXiv2020

Out-of-equilibrium phase diagram of long-range superconductors

Within the ultimate goal of classifying universality in quantum many-body dynamics, understanding the relation between out-of-equilibrium and equilibrium criticality is a crucial objective. Models with power-law interactions exhibit rich well-understood critical behavior in equilibrium, but the out-of-equilibrium picture has remained incomplete, despite recent experimental progress. We construct the rich dynamical phase diagram of free-fermionic chains with power-law hopping and pairing, and provide analytic and numerical evidence showing a direct connection between nonanalyticities of the return rate and zero crossings of the string order parameter. Our results may explain the experimental observation of so-called \textit{accidental} dynamical vortices, which appear for quenches within the same topological phase of the Haldane model, as reported in [Fläschner \textit{et al.}, Nature Physics \textbf{14}, 265 (2018)]. Our work is readily applicable to modern ultracold-atom experiments, not least because state-of-the-art quantum gas microscopes can now reliably measure the string order parameter, which, as we show, can serve as an indicator of dynamical criticality.

cond-mat.stat-mech↗

arXiv2019

Reliability of lattice gauge theories

Currently, there are intense experimental efforts to realize lattice gauge theories in quantum simulators. Except for specific models, however, practical quantum simulators can never be fine-tuned to perfect local gauge invariance. There is thus a strong need for a rigorous understanding of gauge-invariance violation and how to reliably protect against it. As we show through analytic and numerical evidence, in the presence of a gauge invariance-breaking term the gauge violation accumulates only perturbatively at short times before proliferating only at very long times. This proliferation can be suppressed up to infinite times by energetically penalizing processes that drive the dynamics away from the initial gauge-invariant sector. Our results provide a theoretical basis that highlights a surprising robustness of gauge-theory quantum simulators.

cond-mat.quant-gas↗

arXiv2019

Hybrid infinite time-evolving block decimation algorithm for long-range multi-dimensional quantum many-body systems

In recent years, the infinite time-evolution block decimation (iTEBD) method has been demonstrated to be one of the most efficient and powerful numerical schemes for time-evolution in one-dimensional quantum many-body systems. However, a major shortcoming of the method, along with other state-of-the-art algorithms for many-body dynamics, has been their restriction to one spatial dimension. We present an algorithm based on a \textit{hybrid} extension of iTEBD where finite blocks of a chain are first locally time-evolved before an iTEBD-like method combines these processes globally. This in turn permits simulating the dynamics of many-body systems in the thermodynamic limit in $d\geq1$ dimensions including in the presence of long-range interactions. Our work paves the way for simulating the dynamics of many-body phenomena that occur exclusively in higher dimensions, and whose numerical treatments have hitherto been limited to exact diagonalization of small systems, which fundamentally limits a proper investigation of dynamical criticality. We expect the algorithm presented here to be of significant importance to validating and guiding investigations in state-of-the-art ion-trap and ultracold-atom experiments.

cond-mat.str-el↗

arXiv2019

Rapid filling of the spin gap with temperature in the Schwinger-boson mean-field theory of the antiferromagnetic Heisenberg kagome model

Using Schwinger-boson mean-field theory, we calculate the dynamic spin structure factor at low temperatures $0<T\ll J$ for the spin-$1/2$ antiferromagnetic Heisenberg kagome model, within the gapped $\mathbb{Z}_2$ spin liquid phase Ansatz. We find that the spectral gap rapidly fills with temperature, with robust low-energy spectral weight developing by a temperature of $Δ/3$, where the spin gap is $2Δ$ (i.e., $Δ$ is the spinon gap), before any appreciable rise in spinon density or change in zero-temperature mean-field parameters. This is due to deconfinement of spinons which leads to terms suppressed only by $\exp(-Δ/T)$. At still higher temperatures, the spinon density increases rapidly leading to a breakdown of the Schwinger-boson mean-field approach. We suggest that if the impurity-free spectral functions can be obtained through neutron scattering experiments on kagome herbertsmithites, temperature dependence of the subgap weight can provide distinct signatures of a $\mathbb{Z}_2$ quantum spin liquid.

cond-mat.str-el↗

arXiv2019

Dynamical quantum phase transitions in many-body localized systems

We investigate dynamical quantum phase transitions in disordered quantum many-body models that can support many-body localized phases. Employing $l$-bits formalism, we lay out the conditions for which singularities indicative of the transitions appear in the context of many-body localization. Using the combination of the mapping onto $l$-bits and exact diagonalization results, we explicitly demonstrate the presence of these singularities for a candidate model that features many-body localization. Our work paves the way for understanding dynamical quantum phase transitions in the context of many-body localization, and elucidating whether different phases of the latter can be detected from analyzing the former. The results presented are experimentally accessible with state-of-the-art ultracold-atom and ion-trap setups.

cond-mat.stat-mech↗

arXiv2019

Dynamical criticality and domain-wall coupling in long-range Hamiltonians

Dynamical quantum phase transitions hold a deep connection to the underlying equilibrium physics of the quench Hamiltonian. In a recent study [J.~C.~Halimeh \textit{et al.}, arXiv:1810.07187], it has been numerically demonstrated that the appearance of anomalous cusps in the Loschmidt return rate coincides with the presence of bound domain walls in the spectrum of the quench Hamiltonian. Here, we consider transverse-field Ising chains with power-law and exponentially decaying interactions, and show that by removing domain-wall coupling via a truncated Jordan-Wigner transformation onto a Kitaev chain with long-range hopping and pairing, anomalous dynamical criticality is no longer present. This indicates that bound domain walls are necessary for anomalous cusps to appear in the Loschmidt return rate. We also calculate the dynamical phase diagram of the Kitaev chain with long-range hopping and pairing, which in the case of power-law couplings is shown to exhibit rich dynamical criticality including a doubly critical dynamical phase.

cond-mat.stat-mech↗

arXiv2019

Dynamics of multiple atoms in one-dimensional fields

We analyze the dynamics of a set of two-level atoms coupled to the electromagnetic environment within a waveguide. This problem is often tackled by assuming a weak coupling between the atoms and the environment as well as the associated Markov approximation. We show that the accuracy of such an approximation may be more limited than in the single-atom case and also be strongly determined by the presence of collective effects produced by atom-atom interactions. To this aim, we solve the full problem with exact diagonalization and also the time-dependent density matrix renormalization group method, and compare the result to that obtained within a weak-coupling master equation and with the Dicke approximation. Finally, we study the dynamics of the entanglement within the system when considering several inter-atomic distances and atomic frequencies.

quant-ph↗

arXiv2018

Dynamical Quantum Phase Transitions: A Geometric Picture

The Loschmidt echo (LE) is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model (FC-TFIM) as an example, we show that this indeed is not the case, and that a simple semiclassical approximation to systems well described by mean-field theory (MFT) is in fact in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire dynamical phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework. Videos of the post-quench dynamics provided in the supplemental material visualize this new point of view.

cond-mat.stat-mech↗

arXiv2018

Aging dynamics in quenched noisy long-range quantum Ising models

We consider the $d$-dimensional transverse-field Ising model with power-law interactions $J/r^{d+σ}$ in the presence of a noisy longitudinal field with zero average. We study the longitudinal-magnetization dynamics of an initial paramagnetic state after a sudden switch-on of both the interactions and the noisy field. While the system eventually relaxes to an infinite-temperature state with vanishing magnetization correlations, we find that two-time correlation functions show aging at intermediate times. Moreover, for times shorter than the inverse noise strength $κ$ and distances longer than $a(J/κ)^{2/σ}$ with $a$ being the lattice spacing, we find a critical scaling regime of correlation and response functions consistent with the model A dynamical universality class with an initial-slip exponent $θ=1$ and dynamical critical exponent $z=σ/2$. We obtain our results analytically by deriving an effective action for the magnetization field including the noise in a non-perturbative way. The above scaling regime is governed by a non-equilibrium fixed point dominated by the noise fluctuations.

cond-mat.str-el↗

arXiv2018

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of non-analyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of $\mathbb{Z}_2$ symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

cond-mat.stat-mech↗

arXiv2018

Universal equilibrium scaling functions at short times after a quench

By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.

cond-mat.stat-mech↗

arXiv2017

Anomalous dynamical phase in quantum spin chains with long-range interactions

The existence or absence of non-analytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. However, numerical evidence in a recent study [J. C. Halimeh and V. Zauner-Stauber, arXiv:1610.02019] suggests that instead of the trivial phase a distinct anomalous dynamical phase characterized by a novel type of non-analytic cusps occurs in the one-dimensional transverse-field Ising model when interactions are sufficiently long-range. Using an analytic semiclassical approach and exact diagonalization, we show that this anomalous phase also arises in the fully-connected case of infinite-range interactions, and we discuss its defining signature. Our results show that the transition from the regular to the anomalous dynamical phase coincides with Z2-symmetry breaking in the infinite-time limit, thereby showing a connection between two different concepts of dynamical criticality. Our work further expands the dynamical phase diagram of long-range interacting quantum spin chains, and can be tested experimentally in ion-trap setups and ultracold atoms in optical cavities, where interactions are inherently long-range.

cond-mat.stat-mech↗

arXiv2017

Dynamical phase diagram of spin chains with long-range interactions

Using an infinite Matrix Product State (iMPS) technique based on the time-dependent variational principle (TDVP), we study two major types of dynamical phase transitions (DPT) in the one-dimensional transverse-field Ising model (TFIM) with long-range power-law ($\propto1/r^α$ with $r$ inter-spin distance) interactions out of equilibrium in the thermodynamic limit -- \textit{DPT-I}: based on an order parameter in a (quasi-)steady state, and \textit{DPT-II}: based on non-analyticities (cusps) in the Loschmidt-echo return rate. We construct the corresponding rich dynamical phase diagram, whilst considering different quench initial conditions. We find a nontrivial connection between both types of DPT based on their critical lines. Moreover, and very interestingly, we detect a new DPT-II dynamical phase in a certain range of interaction exponent $α$, characterized by what we call \textit{anomalous cusps} that are distinct from the \textit{regular cusps} usually associated with DPT-II. Our results provide the characterization of experimentally accessible signatures of the dynamical phases studied in this work.

cond-mat.stat-mech↗

arXiv2017

Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines

Using the framework of infinite Matrix Product States, the existence of an \textit{anomalous} dynamical phase for the transverse-field Ising chain with sufficiently long-range interactions was first reported in [J.~C.~Halimeh and V.~Zauner-Stauber, arXiv:1610:02019], where it was shown that \textit{anomalous} cusps arise in the Loschmidt-echo return rate for sufficiently small quenches within the ferromagnetic phase. In this work we further probe the nature of the anomalous phase through calculating the corresponding Fisher-zero lines in the complex time plane. We find that these Fisher-zero lines exhibit a qualitative difference in their behavior, where, unlike in the case of the regular phase, some of them terminate before intersecting the imaginary axis, indicating the existence of smooth peaks in the return rate preceding the cusps. Additionally, we discuss in detail the infinite Matrix Product State time-evolution method used to calculate Fisher zeros and the Loschmidt-echo return rate using the Matrix Product State transfer matrix. Our work sheds further light on the nature of the anomalous phase in the long-range transverse-field Ising chain, while the numerical treatment presented can be applied to more general quantum spin chains.

cond-mat.stat-mech↗

arXiv2016

Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition

We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions ($\propto 1/r^α$ with distance $r$), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of $α$ for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on $α$ as well as on the quench parameters.

cond-mat.quant-gas↗