arXiv subjects

Rahul Nandkishore

Publications and source records attributed to Rahul Nandkishore.

At least 37 records · Page 2Linked to original sources

arXiv2024

Playing nonlocal games across a topological phase transition on a quantum computer

Many-body quantum games provide a natural perspective on phases of matter in quantum hardware, crisply relating the quantum correlations inherent in phases of matter to the securing of quantum advantage at a device-oriented task. In this paper we introduce a family of multiplayer quantum games for which topologically ordered phases of matter are a resource yielding quantum advantage. Unlike previous examples, quantum advantage persists away from the exactly solvable point and is robust to arbitrary local perturbations, irrespective of system size. We demonstrate this robustness experimentally on Quantinuum's H1-1 quantum computer by playing the game with a continuous family of randomly deformed toric code states that can be created with constant-depth circuits leveraging mid-circuit measurements and unitary feedback. We are thus able to tune through a topological phase transition - witnessed by the loss of robust quantum advantage - on currently available quantum hardware. This behavior is contrasted with an analogous family of deformed GHZ states, for which arbitrarily weak local perturbations destroy quantum advantage in the thermodynamic limit. Finally, we discuss a topological interpretation of the game, which leads to a natural generalization involving an arbitrary number of players.

quant-ph↗

arXiv2024

Non-local finite-depth circuits for constructing SPT states and quantum cellular automata

Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications of topological phases, as well as the understanding of topological quantum codes, and has obvious relevance for device implementations. Traditionally, this question assumes that the quantum circuit is made up of unitary gates that are geometrically local. Inspired by the advent of noisy intermediate-scale quantum devices, we reconsider this question with $k$-local gates, i.e. gates that act on no more than $k$ degrees of freedom, but are not restricted to be geometrically local. First, we construct explicit finite-depth circuits of symmetric $k$-local gates which create symmetry-protected topological (SPT) states from an initial a product state. Our construction applies both to SPT states protected by global symmetries and subsystem symmetries, but not to those with higher-form symmetries, which we conjecture remain nontrivial. Next, we show how to implement arbitrary translationally invariant quantum cellular automata (QCA) in any dimension using finite-depth circuits of $k$-local gates. These results imply that the topological classifications of SPT phases and QCA both collapse to a single trivial phase in the presence of $k$-local interactions. We furthermore argue that SPT phases are fragile to generic $k$-local symmetric perturbations. We conclude by discussing the implications for other phases, such as fracton phases, and surveying future directions. Our analysis opens a new experimentally motivated conceptual direction examining the stability of phases and the feasibility of state preparation without the assumption of geometric locality.

quant-ph↗

arXiv2023

Current-sensitive Hall effect in a chiral-orbital-current state

Chiral orbital currents (COC) underpin a novel colossal magnetoresistance (CMR) in ferrimagnetic Mn3Si2Te6 [1]. Here we report the Hall effect in the COC state which exhibits the following unprecedented features: (1) A sharp, current-sensitive peak in the magnetic field dependence of the Hall resistivity; (2) An unusually large Hall angle reaching up to 0.15 (comparable to the highest values yet reported); and (3) A current-sensitive scaling relation between the Hall conductivity sigma_xy and the longitudinal conductivity sigma_xx, namely, sigma_xy ~ sigma_xx^alpha with alpha ranging between 3 and 5, which is both sensitive to external current and exceptionally large compared to alpha < 2 typical of most solids. These anomalies point to a giant, current-sensitive Hall effect that is unique to the COC state. We argue that a magnetic field induced by the fully developed COC combines with the applied magnetic field to exert the greatly enhanced transverse force on charge carriers, which dictates the novel Hall responses. The COC Hall effect is unique, as it is generated and controlled via the interaction between intrinsic COC and applied external currents, which leads to novel transport phenomena of fundamental and technological significance and requires new physics for explanation.

cond-mat.str-el↗

arXiv2023

Measurement-induced phases of matter require feedback

We explore universality and phases of matter in hybrid quantum dynamics combining chaotic time evolution and projective measurements. We develop a unitary representation of measurements based on the Stinespring Theorem, which we crucially identify with the time evolution of the system and measurement apparatus, affording significant technical advantages and conceptual insight into hybrid dynamics. We diagnose spectral properties in the presence of measurements for the first time, along with standard, experimentally tractable probes of phase structure, finding no nontrivial effects due to measurements in the absence of feedback. We also establish that nonlinearity in the density matrix is neither sufficient nor necessary to see a transition, and instead identify utilization of the measurement outcomes (i.e., ``feedback'') as the crucial ingredient. After reviewing the definition of a phase of matter, we identify nontrivial orders in adaptive hybrid dynamics -- in which measurement outcomes determine future unitary gates -- finding a genuine measurement-induced absorbing-state phase transition in an adaptive quantum East model. In general, we find that only deterministic and constrained Haar-random dynamics with active feedback and without continuous symmetries can realize genuine, measurement-induced phases of matter.

quant-ph↗

arXiv2023

Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models

We present a set of generalized quantum loop models which provably exhibit topologically stable ergodicity breaking. These results hold for both periodic and open boundary conditions, and derive from a one-form symmetry (notably not being restricted to sectors of extremal one-form charge). We identify simple models in which this one-form symmetry can be emergent, giving rise to the aforementioned ergodicity breaking as an exponentially long-lived prethermal phenomenon. We unveil a web of dualities that connects these models, in certain limits, to models that have previously been discussed in the literature. We also identify nonlocal conserved quantities in such models that correspond to a pattern of system-spanning domain walls, and which are robust to the addition of arbitrary $k$-local perturbations.

cond-mat.stat-mech↗

arXiv2023

Fracton superfluid hydrodynamics

We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest non-trivial setting: a system with charge and dipole symmetry, but without momentum conservation. When no symmetries are broken, our formalism reproduces the quartic subdiffusion ($ω\sim -i k^4$) characteristic of `fracton hydrodynamics' with conserved dipole moment. Our formalism also captures spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is spontaneously broken, the hydrodynamic modes are quadratically propagating and quartically relaxing ($ω\sim \pm k^2 - ik^4$). When the dipole symmetry is spontaneously broken but the charge symmetry is preserved, then we find quadratically relaxing (diffusive) transverse modes, plus another mode which depending on parameters may be either purely diffusive ($ω\sim -i k^2$) or quadratically propagating and quadratically relaxing ($ω\sim \pm k^2 -i k^2$). Our work provides concrete predictions that may be tested in near-term cold atom experiments, and also lays out a general framework that may be applied to study systems with spontaneously broken multipolar symmetries.

cond-mat.stat-mech↗

arXiv2023

Multipole groups and fracton phenomena on arbitrary crystalline lattices

Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the kagome and breathing kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct an effective Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two seemingly novel phenomena, including an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices.

cond-mat.str-el↗

arXiv2022

Extracting spinon self-energies from two-dimensional coherent spectroscopy

Two-dimensional coherent spectroscopy (2DCS) is a nonlinear spectroscopy technique capable of identifying whether apparent continua in linear response are made out of multiplets of sharp deconfined quasiparticles. This makes it a potent tool for experimental identification of fractionalized phases. Previous discussions have focused on limits where the quasiparticles in question are infinitely long lived. In this manuscript we discuss 2DCS in the regime where the fractionalized quasiparticles can themselves decay. We introduce a powerful path integral based approach, whereby the computation of nonlinear susceptibilities reduces to an efficient exercise in diagrammatic perturbation theory. We apply this method to compute the 2DCS response of the one-dimensional transverse field Ising model, in the presence of integrability-breaking perturbations. We discuss aspects of the self-energy of the fractionalized quasiparticles that may be extracted via 2DCS, such as the momentum-dependent decay rate.

cond-mat.str-el↗

arXiv2022

Fracton magnetohydrodynamics

We extend recent work on hydrodynamics with global multipolar symmetries -- known as "fracton hydrodynamics" -- to systems in which the multipolar symmetries are gauged. We refer to the latter as "fracton magnetohydrodynamics", in analogy to conventional magnetohydrodynamics (MHD), which governs systems with gauged charge conservation. We show that fracton MHD arises naturally from higher-rank Maxwell's equations and in systems with one-form symmetries obeying certain constraints; while we focus on "minimal" higher-rank generalizations of MHD that realize diffusion, our methods may also be used to identify other, more exotic hydrodynamic theories (e.g., with magnetic subdiffusion). In contrast to semi-microscopic derivations of MHD, our approach elucidates the origin of the hydrodynamic modes by identifying the corresponding higher-form symmetries. Being rooted in symmetries, the hydrodynamic modes may persist even when the semi-microscopic equations no longer provide an accurate description of the system.

cond-mat.str-el↗

arXiv2022

Random singlet-like phase of disordered Hubbard chains

Local moment formation is ubiquitous in disordered semiconductors such as Si:P, where it is observed both in the metallic and the insulating regimes. Here, we focus on local moment behavior in disordered insulators, which arises from short-ranged, repulsive electron-electron interactions. Using density matrix renormalization group and strong-disorder renormalization group methods, we study paradigmatic models of interacting insulators: one dimensional Hubbard chains with quenched randomness. In chains with either random fermion hoppings or random chemical potentials, both at and away from half-filling, we find exponential decay of charge and fermion 2-point correlations but power-law decay of spin correlations that are indicative of the random singlet phase. The numerical results can be understood qualitatively by appealing to the large-interaction limit of the Hubbard chain, in which a remarkably simple picture emerges.

cond-mat.str-el↗

arXiv2022

Spectroscopic fingerprints of gapless type-II fracton phases

Fracton phases feature elementary excitations with fractionalized mobility and are exciting interest from multiple areas of theoretical physics. However, the most exotic 'type-II' fracton phases, like the Haah codes, currently have no known experimental diagnostics. Here, we explain how type-II fracton phases with gapless gauge modes, such as the $\mathrm{U}(1)$ Haah code, may be identified experimentally. Our analysis makes use of the 'multipole gauge theory' description of type-II fracton phases, which exhibits ultraviolet-infrared (UV-IR) mixing. We show that neutron scattering experiments on gapless type-II fracton phases should generically exhibit exotic pinch points in the structure factor, with distinctive anisotropic contours as a direct consequence of UV-IR mixing. This characteristic pinch point structure provides a clean diagnostic of type-II fracton phases. We also identify distinctive signatures of the (3+1)-D $\mathrm{U}(1)$ Haah code in the low-temperature specific heat.

cond-mat.str-el↗

arXiv2022

Hidden quasiconservation laws in fracton hydrodynamics

We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden "quasiconservation laws", in which certain higher multipole moments can only decay due to dangerously irrelevant corrections to hydrodynamics. We present two simple examples of this phenomenon. Firstly, an isotropic dipole-conserving fluid in the infinite plane conserves an infinite number of "harmonic multipole charges" within linear response; we calculate the decay or growth of these charges due to dangerously irrelevant nonlinearities. Secondly, we consider a model with $xy$ and $x^2-y^2$ quadrupole conservation, in addition to dipole conservation, which is described by isotropic fourth-order subdiffusion, yet has dangerously irrelevant sixth-order corrections necessary to relax the harmonic multipole charges. We confirm our predictions for the anomalously slow decay of the harmonic conserved charges in each setting by using numerical simulations, both of the nonlinear hydrodynamic differential equations, and in quantum automaton circuits on a square lattice.

cond-mat.stat-mech↗

arXiv2022

Hilbert space shattering and dynamical freezing in the quantum Ising model

We discuss quantum dynamics in the transverse field Ising model in two spatial dimensions. We show that, up to a prethermal timescale, which we quantify, the Hilbert space 'shatters' into dynamically disconnected subsectors. We identify this shattering as originating from the interplay of a $\mathrm{U}(1)$ conservation law and a one-form $\mathbb{Z}_2$ constraint. We show that the number of dynamically disconnected sectors is exponential in system volume, and includes a subspace exponential in system volume within which the dynamics is exactly localized, even in the absence of quenched disorder. Depending on the emergent sector in which we work, the shattering can be weak (such that typical initial conditions thermalize with respect to their emergent symmetry sector), or strong (such that typical initial conditions exhibit localized dynamics). We present analytical and numerical evidence that a first order-like 'freezing transition' between weak and strong shattering occurs as a function of the symmetry sector, in a non-standard thermodynamic limit. We further numerically show that on the 'weak' (melted) side of the transition domain wall dynamics follows ordinary diffusion.

cond-mat.stat-mech↗

arXiv2022

Critical localization with Van der Waals interactions

I discuss the quantum dynamics of strongly disordered quantum systems with critically long range interactions, decaying as $1/r^{2d}$ in $d$ spatial dimensions. I argue that, contrary to expectations, localization in such systems is stable at low orders in perturbation theory, giving rise to an unusual `critically many body localized regime.' I discuss the phenomenology of this critical MBL regime, which includes distinctive signatures in entanglement, charge statistics, noise, and transport. Experimentally, such a critically localized regime can be realized in three dimensional systems with Van der Waals interactions, such as Rydberg atoms, and in one dimensional systems with $1/r^2$ interactions, such as trapped ions. I estimate timescales on which high order perturbative and non-perturbative (avalanche) phenomena may destabilize this critically MBL regime, and conclude that the avalanche sets the limiting timescale, in the limit of strong disorder / weak interactions.

cond-mat.dis-nn↗

arXiv2022

Spontaneous breaking of multipole symmetries

Multipole symmetries are of interest both as a window on fracton physics and as a crucial ingredient in realizing new universality classes for quantum dynamics. Here we address the question of whether and when multipole symmetries can be spontaneously broken, both in thermal equilibrium and at zero temperature. We derive generalized Mermin-Wagner arguments for the total or partial breaking of multipolar symmetry groups and generalized Imry-Ma arguments for the robustness of such multipolar symmetry breaking to disorder. We present both general results and explicit examples. Our results should be directly applicable to quantum dynamics with multipolar symmetries and also provide a useful stepping stone to understanding the robustness of fracton phases to thermal fluctuations, quantum fluctuations, and disorder.

cond-mat.stat-mech↗

arXiv2022

Bipolaronic nature of the pseudogap in (TaSe4)2I revealed via weak photoexcitation

The origin of the pseudogap in many strongly correlated materials has been a longstanding puzzle. Here, we uncover which many-body interactions underlie the pseudogap in quasi-one-dimensional (quasi-1D) material (TaSe4)2I by weak photo-excitation of the material to partially melt the ground state order and thereby reveal the underlying states in the gap. We observe the appearance of both dispersive and flat bands by using time- and angle-resolved photoemission spectroscopy. We assign the dispersive band to a single-particle bare band, while the flat band to a collection of single-polaron sub-bands. Our results provide direct experimental evidence that many-body interactions among small Holstein polarons i.e., the formation of bipolarons, are primarily responsible for the pseudogap in (TaSe4)2I. Recent theoretical studies of the Holstein model support the presence of such a bipolaron-to-polaron crossover. We also observe dramatically different relaxation times for the excited in-gap states in (TaSe4)2I (~600 fs) compared with another quasi-1D material Rb0.3MoO3 (~60 fs), which provides a new method for distinguishing between pseudogaps induced by polaronic or Luttinger-liquid many-body interactions.

cond-mat.str-el↗

arXiv2021

Symmetry protected self correcting quantum memory in three space dimensions

Whether self correcting quantum memories can exist at non-zero temperature in a physically reasonable setting remains a great open problem. It has recently been argued [1] that symmetry protected topological (SPT) systems in three space dimensions subject to a strong constraint -- that the quantum dynamics respect a 1-form symmetry -- realize such a quantum memory. We illustrate how this works in Walker-Wang codes, which provide a specific realization of these desiderata. In this setting we show that it is sufficient for the 1-form symmetry to be enforced on a sub-volume of the system which is measure zero in the thermodynamic limit. This strongly suggests that the `SPT' character of the state is not essential. We confirm this by constructing an explicit example with a trivial (paramagnetic) bulk that realizes a self correcting quantum memory. We therefore show that the enforcement of a 1-form symmetry on a measure zero sub-volume of a three dimensional system can be sufficient to stabilize a self correcting quantum memory at non-zero temperature.

quant-ph↗

arXiv2021

Lifetimes of local excitations in disordered dipolar quantum systems

When a strongly disordered system of interacting quantum dipoles is locally excited, the excitation relaxes on some (potentially very long) timescale. We analyze this relaxation process, both for electron glasses with strong Coulomb interactions - in which particle-hole dipoles are emergent excitations - and for systems (e.g., quantum magnets or ultracold dipolar molecules) made up of microscopic dipoles. We consider both energy relaxation rates ($T_1$ times) and dephasing rates ($T_2$ times), and their dependence on frequency, temperature, and polarization. Systems in both two and three dimensions are considered, along with the dimensional crossover in quasi-two dimensional geometries. A rich set of scaling laws is found.

cond-mat.dis-nn↗