Kartiek Agarwal, Sarang Gopalakrishnan, Michael Knap, Markus Mueller, Eugene Demler
We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) Local magnetization fluctuations relax subdiffusively; (ii) the a.c. conductivity vanishes near zero frequency as a power law; (iii) the distribution of resistances becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a Griffiths phase. We establish scaling relations between the associated exponents, using exact linear-response arguments as well as a phenomenological resistor-capacitor model.
Kartiek Agarwal, Ehud Altman, Eugene Demler, Sarang Gopalakrishnan, David A. Huse, Michael Knap
The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.
Prahar Mitra, Matteo Ippoliti, R. N. Bhatt, S. L. Sondhi, Kartiek Agarwal
We describe a quench protocol that allows the rapid preparation of ground states of arbitrary interacting conformal field theories in $1+1$ dimensions. We start from the ground state of a related gapped relativistic quantum field theory and consider sudden quenches along the space-like trajectories $t^2 - x^2 = T^2_0$ (parameterized by $T_0$) to a conformal field theory. Using only arguments of symmetry and conformal invariance, we show that the post-quench stress-energy tensor of the conformal field theory is uniquely constrained up to an overall scaling factor. Crucially, the $\textit{geometry}$ of the quench necessitates that the system approach the vacuum energy density over all space except the singular lines $x = \pm t$. The above arguments are verified using an exact treatment of the quench for the Gaussian scalar field theory (equivalently, the Luttinger liquid), and numerically for the quantum $O(N)$ model in the large-$N$ limit. Additionally, for the Gaussian theory, we find in fact that even when starting from certain excited states, the quench conserves entropy, and is thus also suitable for rapidly preparing excited states. Our methods serve as a fast, alternative route to reservoir-based cooling to prepare quantum states of interest.
Kartiek Agarwal, Eugene Demler, Ivar Martin
We study the `flux noise' spectrum of random-bond quantum Heisenberg spin systems using a real-space renormalization group (RSRG) procedure that accounts for both the renormalization of the system Hamiltonian and of a generic probe that measures the noise. For spin chains, we find that the dynamical structure factor $S_q(f)$, at finite wave-vector $q$, exhibits a power-law behavior both at high and low frequencies $f$, with exponents that are connected to one another and to an anomalous dynamical exponent through relations that differ at $T = 0$ and $T = \infty$. The low-frequency power-law behavior of the structure factor is inherited by any generic probe with a finite band-width and is of the form $1/f^α$ with $0.5 < α< 1$. An analytical calculation of the structure factor, assuming a limiting distribution of the RG flow parameters (spin size, length, bond strength) confirms numerical findings. More generally, we demonstrate that this form of the structure factor, at high temperatures, is a manifestation of anomalous diffusion which directly follows from a generalized spin-diffusion propagator. We also argue that $1/f$-noise is intimately connected to many-body-localization at finite temperatures. In two dimensions, the RG procedure is less reliable; however, it becomes convergent for quasi-one-dimensional geometries where we find that one-dimensional $1/f^α$ behavior is recovered at low frequencies; the latter configurations are likely representative of paramagnetic spin networks that produce $1/f^α$ noise in SQUIDs.
Pierre-Gabriel Rozon, Ning Bao, Kartiek Agarwal
Nov 16, 2023·quant-ph·PDF The classical shadows protocol is an efficient strategy for estimating properties of an unknown state $ρ$ using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from some ensemble and measuring the twirled state in a fixed basis. It was recently shown that for computing local properties, optimal sample complexity (copies of the state required) is remarkably achieved for unitaries drawn from shallow depth circuits composed of local entangling gates, as opposed to purely local (zero depth) or global twirling (infinite depth) ensembles. Here we consider the sample complexity as a function of the depth of the circuit, in the presence of noise. We find that this noise has important implications for determining the optimal twirling ensemble. Under fairly general conditions, we i) show that any single-site noise can be accounted for using a depolarizing noise channel with an appropriate damping parameter $f$; ii) compute thresholds $f_{\text{th}}$ at which optimal twirling reduces to local twirling for arbitrary operators and iii) $n^{\text{th}}$ order Renyi entropies ($n \ge 2$); and iv) provide a meaningful upper bound $t_{\text{max}}$ on the optimal circuit depth for any finite noise strength $f$, which applies to all operators and entanglement entropy measurements. These thresholds strongly constrain the search for optimal strategies to implement shadow tomography and can be easily tailored to the experimental system at hand.
Kartiek Agarwal, R. N. Bhatt, S. L. Sondhi
We propose a spatio-temporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally-moving `front' that $\textit{locally}$ quenches the mass, leaves behind it (in space) a state $\textit{arbitrarily close}$ to the ground state of the gapless model. Importantly, our protocol takes time $\mathcal{O} \left( L \right)$ to produce the ground state of a system of size $\sim L^d$ ($d$ spatial dimensions), while a fully adiabatic protocol requires time $\sim \mathcal{O} \left( L^2 \right)$ to produce a state with exponential accuracy in $L$. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof-of-concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in $d = 1$. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin-chain.
Aidan W. Schiff-Kearn, Lauren Gingras, Simon Bernier, Nima Chamanara, Kartiek Agarwal, Jean-Michel Ménard, David G. Cooke
Relativistically moving dielectric perturbations can be used to manipulate light in new and exciting ways beyond the capabilities of traditional nonlinear optics. Adiabatic interaction with the moving front modulates the wave simultaneously in both space and time, and manifests a front-induced transition in both wave vector and frequency yielding exotic effects including non-reciprocity and time-reversal. Here, we introduce a technique called SLIPSTREAM, Spacetime Light-Induced Photonic STRucturEs for Advanced Manipulation. The technique is based on the creation of relativistic fronts in a semiconductor-filled planar waveguide by photoexcitation of mobile charge carriers. Here we demonstrate the capabilities of SLIPSTREAM for novel manipulation of THz light pulses through relativistic front-induced transitions. In the sub-luminal front velocity regime, we generate temporally stretched THz waveforms, with a quasi-static field lasting for several picoseconds tunable with the front interaction distance. In the super-luminal regime, the carrier front outpaces the THz pulse and a time-reversal operation is performed via a front-induced intra-band transition. We anticipate our platform will be a versatile tool for future applications in the THz spectral band requiring direct and advanced control of light at the sub-cycle level.
Ivar Martin, Kartiek Agarwal
We propose and analyze a family of periodic braiding protocols in systems with multiple localized Majorana modes ($\textit{majoranas}$) for the purposes of Hamiltonian engineering. The protocols rely on double braids$-\textit{draids}-$which flip the signs of both majoranas, as one is taken all the way around the other. Rapid draiding dynamically suppresses some or all inter-majorana couplings. Protocols suppressing all couplings can drastically reduce residual dynamics within the nearly degenerate many-body subspace ("majorana purification") producing more robust computational subspace. Non-trivial topological models can be achieved by selectively applying draids to some of overlapping (imperfect) majoranas. Importantly, draids can be implemented without having to physically braid majoranas or using projective measurements. In particular, draids can be performed by periodically modulating the coupling between a quantum dot and topological superconducting wire to dynamically suppress the hybridization of majoranas by more than an order of magnitude in current experimental setups.
Brett Min, Bastien Fajardo, T. Pereg-Barnea, Kartiek Agarwal
We study a series of dynamical protocols which involve periodically driving a quantum dot coupled to a putative nanowire hosting Majorana zero modes (MZMs) to i) reduce the hybridization between MZMs, ii) improve the coherence of the Majorana qubit with respect to $1/f$ dephasing noise and quasiparticle poisoning, and iii) provide a definitive test to differentiate Andreev Bound states (ABSs) from MZMs. The protocols are based on the notion of $draiding$ - exchanging a pair of Majoranas twice, repeatedly, at high frequency [1]. In this process, the exchanged Majorana operators acquire a robust minus sign such that terms in the Hamiltonian, linear in either operator, vanish on average. The four protocols proposed implement draiding by coupling quantum dot(s) to the end(s) of the nanowire. They are treated using Floquet theory and numerical simulations. The hybridization energy and decoherence rate are shown to be reduced by several orders of magnitude, in accordance with theoretical expectations, when the protocols are implemented on nanowires described by experimentally relevant parameters. The tunneling conductance computed in this Floquet setting reveals zero bias peaks (ZBPs) that become more centered at zero voltage bias. When these protocols are implemented on nanowires supporting ABSs that mimic MZMs in ZBP measurements, the qubit coherence $deteriorates$, in stark contrast to the case where the nanowire supports MZMs and the coherence drastically improves, thus serving as a dynamical test to distinguish MZMs from trivial bound states.
Sujatha Vijayakrishnan, F. Poitevin, Oulin Yu, Z. Berkson-Korenberg, M. Petrescu, M. P Lilly, T. Szkopek, Kartiek Agarwal, K. W. West, L. N. Pfeiffer, G. Gervais
We report low-temperature electronic transport measurements performed in two multi-terminal Corbino samples formed in GaAs/Al-GaAs two-dimensional electron gases (2DEG) with both ultra-high electron mobility ($\gtrsim 20\times 10^6$ $cm^2/Vs)$ and with distinct electron density of $1.7$ and $3.6\times 10^{11}~cm^{-2}$. In both Corbino samples, a non-monotonic behavior is observed in the temperature dependence of the resistance below 1~$K$. Surprisingly, a sharp {\it decrease} in resistance is observed with {\it increasing} temperature in the sample with lower electron density, whereas an opposite behavior is observed in the sample with higher density. To investigate further, transport measurements were performed in large van der Pauw samples having identical heterostructures, and as expected they exhibit resistivity that is monotonic with temperature. Finally, we discuss the results in terms of various lengthscales leading to ballistic and hydrodynamic electronic transport, as well as a possible Gurzhi effect.
Kartiek Agarwal, Emanuele G. Dalla Torre, Jörg Schmiedmayer, Eugene Demler
We study the dynamics of phase relaxation between a pair of one-dimensional condensates created by a bi-directional, supersonic `unzipping' of a finite single condensate. We find that the system fractures into different \emph{extensive} chunks of space-time, within which correlations appear thermal but correspond to different effective temperatures. Coherences between different eigen-modes are crucial for understanding the development of such thermal correlations; at no point in time can our system be described by a generalized Gibbs' ensemble despite nearly always appearing locally thermal. We rationalize a picture of propagating fronts of hot and cold sound waves, populated at effective, relativistically red- and blue-shifted temperatures to intuitively explain our findings. The disparity between these hot and cold temperatures vanishes for the case of instantaneous splitting but diverges in the limit where the splitting velocity approaches the speed of sound; in this limit, a sonic boom occurs wherein the system is excited only along an infinitely narrow, and infinitely hot beam. We expect our findings to apply generally to the study of superluminal perturbations in systems with emergent Lorentz symmetry.
Rohith Sajith, Kartiek Agarwal, Ivar Martin
We examine properties of the mean-field wave function of the one-dimensional Kitaev model supporting Majorana Zero Modes (MZMs) \emph{when restricted} to a fixed number of particles. Such wave functions can in fact be realized as exact ground states of interacting number-conserving Hamiltonians and amount to a more realistic description of the finite isolated superconductors. Akin to their mean-field parent, the fixed-number wave functions encode a single electron spectral function at zero energy that decays exponentially away from the edges, with a localization length that agrees with the mean-field value. Based purely on the structure of the number-projected ground states, we construct the fixed particle number generalization of the MZM operators. They can be used to compute the edge tunneling conductance; however, notably the value of the zero-bias conductance remains the same as in the mean-field case, quantized to $2e^2/h$. We also compute the topological entanglement entropy for the number-projected wave functions and find that it contains a `robust' $\log(2)$ component as well as a logarithmic correction to the mean field result, which depends on the precise partitioning used to compute it. The presence of the logarithmic term in the entanglement entropy indicates the absence of a spectral gap above the ground state; as one introduces fluctuations in the number of particles, the correction vanishes smoothly.
Kartiek Agarwal
Materials hosting topologically protected non-Abelian zero modes offer the exciting possibility of storing and manipulating quantum information in a manner that is protected from decoherence at the hardware level. In this work, we study the possibility of realizing such excitations along line defects in certain fractional quantum Hall states in multi-valley systems. Such line defects have been recently observed experimentally between valley polarized Hall states on the surface of Bi(111), and excitations near these defects appear to be gapped (gapless) depending on the presence (absence) of interaction-induced gapping perturbations constrained by momentum selection rules, while the position of defects is determined by strain. In this work, we use these selection rules to show that a hybrid structure involving a superlattice imposed on such a multi-valley quantum Hall surface realizes non-Abelian anyons which can then be braided by modulating strain locally to move line defects. Specifically, we explore such defects in Abelian fractional quantum Hall states of the form ν = 2/m using a K-matrix approach, and identify relevant gapping perturbations. Charged modes on these line defects remain gapped, while charge netural valley pseudospin modes may be gapped with the aid of two (mutually orthogonal) superlattices which pin non-commuting fields. When these superlattices are alternated along the line defect, non-Abelian zero modes result at points where the gapping perturbation changes. Given that these pseudospin modes carry no net physical charge or spin, the setup eschews utilizing superconducting and magnetic elements to engineer gapping perturbations. We provide a scheme to braid these modes using strain modulation, and confirm that the resulting unitaries satisfy a representation of the braid group.
Kartiek Agarwal, Ivar Martin, Mikhail D. Lukin, Eugene Demler
While two levels systems (TLSs) are ubiqitous in solid state systems, microscopic understanding of their nature remains an outstanding problem. Conflicting phenomenological models are used to describe TLSs in seemingly similar materials when probed with different experimental techniques. Specifically, bulk measurements in amorphous solids have been interpreted using the model of a tunneling atom or group of atoms, whereas TLSs observed in the insulating barriers of Josephson junction qubits have been understood in terms of tunneling of individual electrons. Motivated by recent experiments studying TLSs in Josephson junctions, especially the effects of elastic strain on TLS properties, we analyze interaction of the electronic TLS with phonons. We demonstrate that strong polaronic effects lead to dramatic changes in TLS properties. Our model gives a quantitative understanding of the TLS relaxation and dephasing as probed in Josephson junction qubits, while providing an alternative interpretation of bulk experiments. We demonstrate that a model of polaron dressed electronic TLS leads to estimates for the density and distribution of parameters of TLSs consistent with bulk experiments in amorphous solids. This model explains such surprising observations of recent experiments as the existence of minima in the energy of some TLSs as a function of strain and makes concrete predictions for the character of TLS dephasing near such minima. We argue that better understanding of the microscopic nature of TLSs can be used to improve properties of quantum devices, from an enhancement of relaxation time of TLSs, to creating new types of strongly interacting optomechanical systems.
Kartiek Agarwal, Mallika T. Randeria, A. Yazdani, S. L. Sondhi, S. A. Parameswaran
We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunnelling microscopy experiments on Bi(111) surfaces. We show that the domain wall properties depend sensitively on the filling factor $ν$ of the underlying (integer) quantum Hall states. For $ν=1$ and in the absence of impurity scattering we argue that the wall hosts a single-channel Luttinger liquid whose gaplessness is a consequence of valley and charge conservation. For $ν=2$, it supports a two-channel Luttinger liquid, which for sufficiently strong interactions enters a symmetry-preserving thermal metal phase with a charge gap coexisting with gapless neutral intervalley modes. The domain wall physics in this state is identical to that of a bosonic topological insulator protected by $U(1)\times U(1)$ symmetry, and we provide a formal mapping between these problems. We discuss other unusual properties and experimental signatures of these `anomalous' one-dimensional systems.
Kartiek Agarwal, Sriram Ganeshan, R. N. Bhatt
We study localization and charge dynamics in a monochromatically driven one-dimensional Anderson insulator focussing on the low-frequency, strong-driving regime. We study this problem using a mapping of the Floquet Hamiltonian to a hopping problem with correlated disorder in one higher harmonic-space dimension. We show that (i) resonances in this model correspond to \emph{adiabatic} Landau-Zener (LZ) transitions that occur due to level crossings between lattice sites over the course of dynamics; (ii) the proliferation of these resonances leads to dynamics that \emph{appear} diffusive over a single drive cycle, but the system always remains localized; (iii) actual charge transport occurs over many drive cycles due to slow dephasing between these LZ orbits and is logarithmic-in-time, with a crucial role being played by far-off Mott-like resonances; and (iv) applying a spatially-varying random phase to the drive tends to decrease localization, suggestive of weak-localization physics. We derive the conditions for the strong driving regime, determining the parametric dependencies of the size of Floquet eigenstates, and time-scales associated with the dynamics, and corroborate the findings using both numerical scaling collapses and analytical arguments.
Suman Jyoti De, Tami Pereg-Barnea, Kartiek Agarwal
Nanoscale defects such as Nitrogen Vacancy (NV) centers can serve as sensitive and non-invasive probes of electromagnetic fields and fluctuations from materials, which in turn can be used to characterize these systems. Here we specifically discuss how NV centers can probe time-reversal symmetry breaking (TRSB) phenomena in low-dimensional conductors. We argue that the difference in relaxation rates $Γ_{\pm \hat{z}}$ of NV centers starting from $m = \pm 1$ spin states to the ground state with $m = 0$ directly probes TRSB. The effect arises from the difference in the fluctuation spectrum of left and right-polarized electromagnetic fields emanating from such materials. In the quantum Hall setting, the NV center experiences (nearly zero) large additional contribution to its relaxation due to the presence of the material when its magnetic dipole (anti-) aligns with the external field. More generally, the difference in the relaxation rates is sensitive to the imaginary part of the wave-vector dependent Hall conductivity. We argue that this can be used to determine the Hall viscosity, which can potentially distinguish candidate fractional quantum Hall states and be used to infer the pairing angular momentum in TRSB superconductors. For the latter, we consider specifically the case of TRSB in stacked twisted Bismuth strontium calcium copper oxide (BSCCO) flakes, which have recently been investigated experimentally and are suggested to exhibit TRSB. We show that the average relaxation rate $\left[Γ_{+\hat{z}} + Γ_{-\hat{z}}\right]$ near such a system exhibits a Hebel-Slichter like enhancement below $T_c$. The difference $Γ_{+\hat{z}} - Γ_{-\hat{z}}$ also inherits this peak but is only non-zero for $T < T_c$ and only in a chiral d-wave superconductor. We provide concrete estimates for observing this effect.
Pierre-Gabriel Rozon, Michael J. Gullans, Kartiek Agarwal
Dec 22, 2021·quant-ph·PDF We provide a systematic approach for constructing approximate quantum many-body scars (QMBS) starting from two-layer Floquet automaton circuits that exhibit trivial many-body revivals. We do so by applying successively more restrictions that force local gates of the automaton circuit to commute concomitantly more accurately when acting on select scar states. With these rules in place, an effective local, Floquet Hamiltonian is seen to capture dynamics of the automaton over a long prethermal window. We provide numerical evidence for such a picture and use our construction to derive several QMBS models, including the celebrated PXP model.
Kartiek Agarwal, Ivar Martin
We construct a dynamical decoupling protocol for accurately generating local and global symmetries in general many-body systems. Multiple commuting and non-commuting symmetries can be created by means of a self-similar-in-time ("polyfractal") drive. The result is an effective Floquet Hamiltonian that remains local and avoids heating over exponentially long times. This approach can be used to realize a wide variety of quantum models, and non-equilibrium quantum phases.
Kartiek Agarwal, Ning Bao
We investigate a plausible route to resolving the black hole information paradox by examining the effects of decoherence on Hawking radiation. In particular, we show that a finite but non-zero rate of decoherence can lead to efficient extraction of information from the evaporating black hole. This effectively pushes the paradox from becoming manifest at the Page time when the black hole has evaporated to half its size, to a timescale solely determined by the rate of decoherence. If this rate is due to a putative interaction with gravitons, the black hole at this timescale can be expected to be Planck-sized, but notably without an extensive amount of information packed inside. We justify our findings by numerically studying a toy model of stabilizer circuits that can efficiently model black hole evaporation in the presence of decoherence. The latter is found to be well described by an effective rate equation for the entanglement and which corroborates our findings.