arXiv subjects

Michael Schecter

Publications and source records attributed to Michael Schecter.

At least 19 recordsLinked to original sources

arXiv2025

Feasibility Study of 3D-Printed Micro Junction Array for Ion Trap Quantum Processor

We introduce an ion trap platform based on a 3D-printed micro-junction array, designed to implement quantum charge-coupled device (QCCD) architectures for large-scale quantum information processing (QIP). The integration of three-dimensionally structured micro Radio-Frequency (RF) electrodes above a surface-electrode trap enables flexible control of electric field profiles across both linear and junction regions. Through simulations, we demonstrate that the linear region exhibits deeper and more harmonic ion confinement with reduced RF drive power compared to conventional planar traps. Crucially, we identify a junction geometry that maintains uniform ion confinement during transport while substantially reducing the pseudopotential barrier. This reduction facilitates low-heating, high-fidelity transport of single- and multi-species ion crystals. Our results establish a viable route toward fault-tolerant quantum computing by enabling modular and scalable QCCD systems based on the state-of-the-art 3D-printing technologies.

quant-ph↗

arXiv2025

Digital quantum magnetism on a trapped-ion quantum computer

Digital quantum matter -- realized when discrete quantum gates approximate continuous time evolution -- is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviors observed in equilibrium systems, ranging from the nontrivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here, we use Quantinuum's system model H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics due to approximate energy conservation, and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of $99.94(1)\%$), and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.

quant-ph↗

arXiv2024

The computational power of random quantum circuits in arbitrary geometries

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of $\sim 50$ qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe recent hardware upgrades to Quantinuum's H2 quantum computer enabling it to operate on up to $56$ qubits with arbitrary connectivity and $99.843(5)\%$ two-qubit gate fidelity. Utilizing the flexible connectivity of H2, we present data from random circuit sampling in highly connected geometries, doing so at unprecedented fidelities and a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. The considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture as continued progress is made towards building larger machines.

quant-ph↗

arXiv2019

Quantum Many-Body Scar States with Emergent Kinetic Constraints and Finite-Entanglement Revivals

We construct a set of exact, highly excited eigenstates for a nonintegrable spin-1/2 model in one dimension that is relevant to experiments on Rydberg atoms in the antiblockade regime. These states provide a new solvable example of quantum many-body scars: their sub-volume-law entanglement and equal energy spacing allow for infinitely long-lived coherent oscillations of local observables following a suitable quantum quench. While previous works on scars have interpreted such oscillations in terms of the precession of an emergent macroscopic SU(2) spin, the present model evades this description due to a set of emergent kinetic constraints in the scarred eigenstates that are absent in the underlying Hamiltonian. We also analyze the set of initial states that give rise to periodic revivals, which persist as approximate revivals on a finite timescale when the underlying model is perturbed. Remarkably, a subset of these initial states coincides with the family of area-law entangled Rokhsar-Kivelson states shown by Lesanovsky to be exact ground states for a class of models relevant to experiments on Rydberg-blockaded atomic lattices.

cond-mat.str-el↗

arXiv2019

Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets

We study the spin-1 XY model on a hypercubic lattice in $d$ dimensions and show that this well-known nonintegrable model hosts an extensive set of anomalous finite-energy-density eigenstates with remarkable properties. Namely, they exhibit subextensive entanglement entropy and spatiotemporal long-range order, both believed to be impossible in typical highly excited eigenstates of nonintegrable quantum many-body systems. While generic initial states are expected to thermalize, we show analytically that the eigenstates we construct lead to weak ergodicity breaking in the form of persistent oscillations of local observables following certain quantum quenches--in other words, these eigenstates provide an archetypal example of so-called "quantum many-body scars." This work opens the door to the analytical study of the microscopic origin, dynamical signatures, and stability of such phenomena.

cond-mat.str-el↗

arXiv2019

Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation

We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body oscillations were observed only when the system was initialized in a particular product state. This pronounced coherence has been attributed to the presence of special "scarred" eigenstates with nearly equally-spaced energies and putative nonergodic properties despite their finite energy density. In this paper we uncover a surprising connection between these scarred eigenstates and low-lying quasiparticle excitations of the spin chain. In particular, we show that these eigenstates can be accurately captured by a set of variational states containing a macroscopic number of magnons with momentum $\pi$. This leads to an interpretation of the scarred eigenstates as finite-energy-density condensates of weakly interacting $\pi$-magnons. One natural consequence of this interpretation is that the scarred eigenstates possess long-range order in both space and time, providing a rare example of the spontaneous breaking of continuous time-translation symmetry. We verify numerically the presence of this space-time crystalline order and explain how it is consistent with established no-go theorems precluding its existence in ground states and at thermal equilibrium.

cond-mat.str-el↗

arXiv2019

Interplay between Magnetic and Vestigial Nematic Orders in the Layered $J_1$-$J_2$ Classical Heisenberg Model

We study the layered $J_1$-$J_2$ classical Heisenberg model on the square lattice using a self-consistent bond theory. We derive the phase diagram for fixed $J_1$ as a function of temperature $T$, $J_2$ and interplane coupling $J_z$. Broad regions of (anti)ferromagnetic and stripe order are found, and are separated by a first-order transition near $J_2\approx 0.5$ (in units of $|J_1|$). Within the stripe phase the magnetic and vestigial nematic transitions occur simultaneously in first-order fashion for strong $J_z$. For weaker $J_z$ there is in addition, for $J_2^*<J_2 < J_2^{**}$, an intermediate regime of split transitions implying a finite temperature region with nematic order but no long-range stripe magnetic order. In this split regime, the order of the transitions depends sensitively on the deviation from $J_2^*$ and $J_2^{**}$, with split second-order transitions predominating for $J_2^* \ll J_2 \ll J_2^{**}$. We find that the value of $J_2^*$ depends weakly on the interplane coupling and is just slightly larger than $0.5$ for $|J_z| \lesssim 0.01$. In contrast the value of $J_2^{**}$ increases quickly from $J_2^*$ at $|J_z| \lesssim 0.01$ as the interplane coupling is further reduced. In addition, the magnetic correlation length is shown to directly depend on the nematic order parameter and thus exhibits a sharp increase (or jump) upon entering the nematic phase. Our results are broadly consistent with predictions based on itinerant electron models of the iron-based superconductors in the normal-state, and thus help substantiate a classical spin framework for providing a phenomenological description of their magnetic properties.

cond-mat.str-el↗

arXiv2018

Configuration-Controlled Many-Body Localization and the Mobility Emulsion

We uncover a new non-ergodic phase, distinct from the many-body localized (MBL) phase, in a disordered two-leg ladder of interacting hardcore bosons. The dynamics of this emergent phase, which has no single-particle analog and exists only for strong disorder and finite interaction, is determined by the many-body configuration of the initial state. Remarkably, this phase features the $\textit{coexistence}$ of localized and extended many-body states at fixed energy density and thus does not exhibit a many-body mobility edge, nor does it reduce to a model with a single-particle mobility edge in the noninteracting limit. We show that eigenstates in this phase can be described in terms of interacting emergent Ising spin degrees of freedom ("singlons") suspended in a mixture with inert charge degrees of freedom ("doublons" and "holons"), and thus dub it a $\textit{mobility emulsion}$ (ME). We argue that grouping eigenstates by their doublon/holon density reveals a transition between localized and extended states that is invisible as a function of energy density. We further demonstrate that the dynamics of the system following a quench may exhibit either thermalizing or localized behavior depending on the doublon/holon density of the initial product state. Intriguingly, the ergodicity of the ME is thus tuned by the initial state of the many-body system. These results establish a new paradigm for using many-body configurations as a tool to study and control the MBL transition. The ME phase may be observable in suitably prepared cold atom optical lattices.

cond-mat.dis-nn↗

arXiv2018

Quantum Inverse Freezing and Mirror-Glass Order

It is well-known that spontaneous symmetry breaking in one spatial dimension is thermodynamically forbidden at finite energy density. Here we show that mirror-symmetric disorder in an interacting quantum system can invert this paradigm, yielding spontaneous breaking of mirror symmetry only at finite energy density and giving rise to "mirror-glass" order. The mirror-glass transition, which is driven by a finite density of interacting excitations, is enabled by many-body localization, and appears to occur simultaneously with the localization transition. This counterintuitive manifestation of localization-protected order can be viewed as a quantum analog of inverse freezing, a phenomenon that occurs, e.g., in certain models of classical spin glasses.

cond-mat.dis-nn↗

arXiv2018

Many-Body Spectral Reflection Symmetry and Protected Infinite-Temperature Degeneracy

Protected zero modes in quantum physics traditionally arise in the context of ground states of many-body Hamiltonians. Here we study the case where zero modes exist in the center of a reflection-symmetric many-body spectrum, giving rise to the notion of a protected "infinite-temperature" degeneracy. For a certain class of nonintegrable spin chains, we show that the number of zero modes is determined by a chiral index that grows exponentially with system size. We propose a dynamical protocol, feasible in ongoing experiments in Rydberg atom quantum simulators, to detect these many-body zero modes and their protecting spectral reflection symmetry. Finally, we consider whether the zero energy states obey the eigenstate thermalization hypothesis, as is expected of states in the middle of the many-body spectrum. We find intriguing differences in their eigenstate properties relative to those of nearby nonzero-energy eigenstates at finite system sizes.

cond-mat.str-el↗

arXiv2017

Cooper Pair Induced Frustration and Nematicity of Two-Dimensional Magnetic Adatom Lattices

We propose utilizing the Cooper pair to induce magnetic frustration in systems of two-dimensional (2D) magnetic adatom lattices on s-wave superconducting surfaces. The competition between singlet electron correlations and the RKKY coupling is shown to lead to a variety of hidden order states that break the point-group symmetry of the 2D adatom lattice at finite temperature. The phase diagram is constructed using a newly developed effective bond theory [M. Schecter et al., Phys. Rev. Lett. 119, 157202 (2017)], and exhibits broad regions of long-range vestigial nematic order.

cond-mat.str-el↗

arXiv2017

Nematic Bond Theory of Heisenberg Helimagnets

We study classical two-dimensional frustrated Heisenberg models with generically incommensurate groundstates. A new theory for the spin-nematic "order by disorder" transition is developed based on the self-consistent determination of the effective exchange coupling bonds. In our approach, fluctuations of the constraint field imposing conservation of the local magnetic moment drive nematicity at low temperatures. The critical temperature is found to be highly sensitive to the peak helimagnetic wavevector, and vanishes continuously when approaching rotation symmetric Lifshitz points. Transitions between symmetry distinct nematic orders may occur by tuning the exchange parameters, leading to lines of bicritical points.

cond-mat.str-el↗

arXiv2016

Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

We investigate the formation of a new type of composite topological excitation -- the skyrmion-vortex pair (SVP) -- in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed, and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulations. Furthermore, we develop a semiclassical description of the coupled skyrmion-vortex dynamics and discuss how SVPs can be controlled by applied spin currents.

cond-mat.mes-hall↗

arXiv2016

Quantum impurities: from mobile Josephson junctions to depletons

We overview the main features of mobile impurities moving in one-dimensional superfluid backgrounds by modeling it as a mobile Josephson junction, which leads naturally to the periodic dispersion of the impurity. The dissipation processes, such as radiative friction and quantum viscosity, are shown to result from the interaction of the collective phase difference with the background phonons. We develop a more realistic depleton model of an impurity-hole bound state that provides a number of exact results interpolating between the semiclassical weakly-interacting picture and the strongly interacting Tonks-Girardeau regime. We also discuss the physics of a trapped impurity, relevant to current experiments with ultra cold atoms.

cond-mat.quant-gas↗

arXiv2015

Spin-lattice order in one-dimensional conductors: beyond the RKKY effect

We investigate magnetic order in a lattice of classical spins coupled to an isotropic gas of one-dimensional (1d) conduction electrons via local exchange interactions. The frequently discussed Ruderman-Kittel-Kasuya-Yosida (RKKY) effective exchange model for this system predicts that spiral order is always preferred. Here we consider the problem nonperturbatively, and find that such order vanishes above a critical value of the exchange coupling that depends strongly on the lattice spacing. The critical coupling tends to zero as the lattice spacing becomes commensurate with the Fermi wave vector, signalling the breakdown of the perturbative RKKY picture, and spiral order, even at weak coupling. We provide the exact phase diagram for arbitrary exchange coupling and lattice spacing, and discuss its stability. Our results shed new light on the problem of utilizing a spiral spin-lattice state to drive a one-dimensional superconductor into a topological phase.

cond-mat.mes-hall↗

arXiv2014

Comment on "Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas"

In a recent paper, arxiv:1402.6362, Gamayun, Lychkovskiy, and Cheianov studied the dynamics of a mobile impurity embedded into a one-dimensional Tonks-Girardeau gas of strongly interacting bosons. Employing the Boltzmann equation approach, they arrived at the following main conclusions: (i) a light impurity, being accelerated by a constant force does not exhibit Bloch oscillations; (ii) a heavy impurity does undergo Bloch oscillations, accompanied by a drift with the velocity proportional to the square root of force. In this comment we argue that the result (i) is an artifact of the classical Boltzmann approximation, which misses the formation of the (quasi) bound-state between the impurity and a hole. Result (ii), while not valid at asymptotically small force, indeed reflects an interesting intermediate-force behavior. Here we clarify its limits of applicability and extend beyond the Tonks-Girardeau limit.

cond-mat.quant-gas↗

arXiv2013

Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids

Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as $1/r^3$, much slower than the van der Waals interaction $\sim1/r^6$, where $r$ is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.

cond-mat.quant-gas↗

arXiv2012

Forming doublons by a quantum quench

Repulsive interactions between particles on a lattice may lead to bound states, so called doublons. Such states may be created by dynamically tuning the interaction strength, e.g. using a Feshbach resonance, from attraction to repulsion. We study the doublon production efficiency as a function of the tuning rate at which the on-site interaction is varied. An expectation based on the Landau- Zener law suggests that exponentially few doublons are created in the adiabatic limit. Contrary to such an expectation, we found that the number of produced doublons scales as a power law of the tuning rate with the exponent dependent on the dimensionality of the lattice. The physical reason for this anomaly is the effective decoupling of doublons from the two-particle continuum for center of mass momenta close to the corners of the Brillouin zone. The study of doublon production may be a sensitive tool to extract detailed information about the band structure.

cond-mat.quant-gas↗