arXiv subjects

Anushya Chandran

Publications and source records attributed to Anushya Chandran.

At least 55 records · Page 3Linked to original sources

arXiv2020

Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit

Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. We measure the evolution of trajectories of two quantum states, initially prepared at nearby points in synthetic phase space. We detect the synthetic Hall effect through the predicted overlap oscillations at a quantized fundamental frequency proportional to the Chern number, which characterizes the topological phases of the system. We further observe half-quantization of the Chern number at the transition between the synthetic Hall regime and the trivial regime, and the associated concentration of local Berry curvature in synthetic phase space. Our work opens up the possibility of using driven qubits to design and study higher-dimensional topological insulators and semi-metals in synthetic dimensions.

cond-mat.mes-hall↗

arXiv2020

Integrability and dark states in an anisotropic central spin model

Central spin models describe a variety of quantum systems in which a spin-1/2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond. We show that the fully anisotropic central spin Hamiltonian with (XX) Heisenberg interactions is integrable. Building on the class of integrable Richardson-Gaudin models, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. These states divide into two exponentially large classes: bright states, where the qubit is entangled with the bath, and dark states, where it is not. We discuss how dark states limit qubit-assisted spin bath polarization and provide a robust long-lived quantum memory for qubit states.

cond-mat.str-el↗

arXiv2019

Do Rydberg chains yield Fibonacci anyons?

Recent experiments have focused attention on the properties of chains of atoms in which the atoms are either in their ground states or in highly excited Rydberg states which block similar excitations in their immediate neighbors. As the low energy Hilbert space of such chains is isomorphic to that of a chain of Fibonacci anyons, they have been proposed as a platform for topological quantum computation and for simulating anyon dynamics. We show that generic local operators in the Rydberg chain correspond to non-local anyonic operators that do not preserve a topological symmetry of the physical anyons. Consequently, we argue that Rydberg chains do not yield Fibonacci anyons and quantum computation with Rydberg atoms is not topologically protected.

quant-ph↗

arXiv2019

Signatures of integrability in the dynamics of Rydberg-blockaded chains

A recent experiment on a 51-atom Rydberg blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this article, we show that the experimental Hamiltonian exhibits non-thermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The unconventional quench dynamics in the parent model could signal a novel class of integrable system.

cond-mat.str-el↗

arXiv2019

Swift heat transfer by fast-forward driving in open quantum systems

Typically, time-dependent thermodynamic protocols need to run asymptotically slowly in order to avoid dissipative losses. By adapting ideas from counter-diabatic driving and Floquet engineering to open systems, we develop fast-forward protocols for swiftly thermalizing a system oscillator locally coupled to an optical phonon bath. These protocols control the system frequency and the system-bath coupling to induce a resonant state exchange between the system and the bath. We apply the fast-forward protocols to realize a fast approximate Otto engine operating at high power near the Carnot Efficiency. Our results suggest design principles for swift cooling protocols in coupled many-body systems.

quant-ph↗

arXiv2018

Universal entanglement of typical states in constrained systems

Local constraints play an important role in the effective description of many quantum systems. Their impact on dynamics and entanglement thermalization are just beginning to be unravelled. We develop a large $N$ diagrammatic formalism to exactly evaluate the bipartite entanglement of random pure states in large constrained Hilbert spaces. The resulting entanglement spectra may be classified into `phases' depending on their singularities. Our closed solution for the spectra in the simplest class of constraints reveals a non-trivial phase diagram with a Marchenko-Pastur (MP) phase which terminates in a critical point with new singularities. The much studied Rydberg-blockaded/Fibonacci chain lies in the MP phase with a modified Page correction to the entanglement entropy, $ΔS_1 = 0.513595\cdots$. Our results predict the entanglement of infinite temperature eigenstates in thermalizing constrained systems and provide a baseline for numerical studies.

quant-ph↗

arXiv2018

Topological classification of quasi-periodically driven quantum systems

Few level quantum systems driven by $n_\mathrm{f}$ incommensurate fundamental frequencies exhibit temporal analogues of non-interacting phenomena in $n_\mathrm{f}$ spatial dimensions, a consequence of the generalisation of Floquet theory in frequency space. We organise the fundamental solutions of the frequency lattice model for $n_\mathrm{f}=2$ into a quasi-energy band structure and show that every band is classified by an integer Chern number. In the trivial class, all bands have zero Chern number and the quasi-periodic dynamics is qualitatively similar to Floquet dynamics. The topological class with non-zero Chern bands has dramatic dynamical signatures, including the pumping of energy from one drive to the other, chaotic sensitivity to initial conditions, and aperiodic time dynamics of expectation values. The topological class is however unstable to generic perturbations due to exact level crossings in the quasi-energy spectrum. Nevertheless, using the case study of a spin in a quasi-periodically varying magnetic field, we show that topological class can be realised at low frequencies as a pre-thermal phase, and at finite frequencies using counter-diabatic tools.

cond-mat.mes-hall↗

arXiv2017

How does a locally constrained quantum system localize?

At low energy, the dynamics of excitations of many physical systems are locally constrained. Examples include frustrated anti-ferromagnets, fractional quantum Hall fluids and Rydberg atoms in the blockaded regime. Can such locally constrained systems be fully many-body localized (MBL)? In this article, we answer this question affirmatively and elucidate the structure of the accompanying quasi-local integrals of motion. By studying disordered spin chains subject to a projection constraint in the $z$-direction, we show that full MBL is stable at strong $z$-field disorder and identify a new mechanism of localization through resonance at strong transverse disorder. However MBL is not guaranteed; the constraints can `frustrate' the tendency of the spins to align with the transverse fields and lead to full thermalization or criticality. We further provide evidence that the transition is discontinuous in local observables with large sample-to-sample variations. Our study has direct consequences for current quench experiments in Rydberg atomic chains.

cond-mat.dis-nn↗

arXiv2017

Localization and symmetry breaking in the quantum quasiperiodic Ising glass

Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a \emph{quasiperiodic Ising glass} stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero temperature phase diagram is also surprisingly rich, consisting of paramagnetic, ferromagnetic and quasiperiodically alternating ground state phases with extended, localized and critically delocalized low energy excitations. The system exhibits an unusual quantum Ising transition whose properties are intermediate between those of the clean and infinite randomness Ising transitions. Many of these results follow from a geometric generalization of the Aubry-André duality which we develop. The quasiperiodic Ising glass may be realized in near term quantum optical experiments.

cond-mat.dis-nn↗

arXiv2016

Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice

A quantum critical (QC) fluid exhibits universal subleading corrections to the area law of its entanglement entropies. In two dimensions when the partition involves a corner of angle $θ$, the subleading term is logarithmic with coefficient $a_α(θ)$ for the $α$-Rényi entropy. In the smooth limit $θ\!\to\!π$, $a_1(θ)$ yields the central charge of the stress tensor when the QC point is described by a conformal field theory (CFT). For general Rényi indices and angles, $a_α(θ)$ is richer and few general results exist. We study $a_α(θ)$ focusing on two benchmark CFTs, the free Dirac fermion and boson. We perform numerical lattice calculations to obtain high precision results in $θ,α$ regimes hitherto unexplored. We derive field theory estimates for $a_α(θ)$, including new exact results, and demonstrate an excellent quantitative match with our numerical calculations. We also develop and test strong lower bounds, which apply to both free and interacting QC systems. Finally, we comment on the near collapse of $a_α(θ)$ for various theories, including interacting $O(N)$ models.

cond-mat.str-el↗

arXiv2015

When is an area law not an area law?

Entanglement entropy is typically proportional to area, but sometimes it acquires an additional logarithmic pre-factor. We offer some intuitive explanations for these facts.

hep-th↗

arXiv2015

Emergent Coulombic criticality and Kibble-Zurek scaling in a topological magnet

When a classical system is driven through a continuous phase transition, its nonequilibrium response is universal and exhibits Kibble-Zurek scaling. We explore this dynamical scaling in the novel context of a three-dimensional topological magnet with fractionalized excitations, namely the liquid-gas transition of the emergent mobile magnetic monopoles in dipolar spin ice. Using field-mixing and finite-size scaling techniques, we place the critical point of the liquid-gas line in the three-dimensional Ising universality class. We then demonstrate Kibble-Zurek scaling for sweeps of the magnetic field through the critical point. Unusually slow microscopic time scales in spin ice offer a unique opportunity to detect this universal nonequilibrium physics in current experimental setups.

cond-mat.str-el↗

arXiv2015

Interaction stabilized steady states in the driven O(N) model

We study periodically driven bosonic scalar field theories in the infinite N limit. It is well-known that the free theory can undergo parametric resonance under monochromatic modulation of the mass term and thereby absorb energy indefinitely. Interactions in the infinite N limit terminate this increase for any choice of the UV cutoff and driving frequency. The steady state has non-trivial correlations and is synchronized with the drive. The O(N) model at infinite N provides the first example of a clean interacting quantum system that does not heat to infinite temperature at any drive frequency.

cond-mat.stat-mech↗

arXiv2015

A semi-classical limit for the many-body localization transition

We introduce a semi-classical limit for many-body localization in the absence of global symmetries. Microscopically, this limit is realized by disordered Floquet circuits composed of Clifford gates. In $d=1$, the resulting dynamics are always many-body localized with a complete set of strictly local integrals of motion. In $d\geq 2$, the system realizes both localized and delocalized phases separated by a continuous transition in which ergodic puddles percolate. We argue that the phases are stable to deformations away from the semi-classical limit and estimate the resulting phase boundary. The Clifford circuit model is a distinct tractable limit from that of free fermions and suggests bounds on the critical exponents for the generic transition.

cond-mat.dis-nn↗

arXiv2015

Periodically driven ergodic and many-body localized quantum systems

We study dynamics of isolated quantum many-body systems under periodic driving. We consider a driving protocol in which the Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem in energy space. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We argue that our results hold for general driving protocols, and discuss their experimental implications.

cond-mat.dis-nn↗

arXiv2014

Local integrals of motion and the logarithmic lightcone in many-body localized systems

We propose to define full many-body localization in terms of the recently introduced integrals of motion[Chandran et al., arXiv:1407.8480], which characterize the time-averaged response of the system to a local perturbation. The quasi-locality of such integrals of motion implies an effective lightcone that grows logarithmically in time. This subsequently implies that (i) the average entanglement entropy can grow at most logarithmically in time for a global quench from a product state, and (ii) with high probability, the time evolution of a local operator for a time interval $|t|$ can be classically simulated with a resource that scales polynomially in $|t|$.

cond-mat.dis-nn↗

arXiv2014

Constructing local integrals of motion in the many-body localized phase

Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body localized (MBL) systems are characterized by extensively many local integrals of motion (LIOM), which underlie the absence of transport and thermalization in these systems. Here we report a physically motivated construction of local integrals of motion in the MBL phase. We show that any local operator (e.g., a local particle number or a spin flip operator), evolved with the system's Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such operators have a clear physical meaning, describing the response of the MBL system to a local perturbation. In particular, when a local operator represents a density of some globally conserved quantity, the corresponding LIOM describes how this conserved quantity propagates through the MBL phase. Being uniquely defined and experimentally measurable, these LIOMs provide a natural tool for characterizing the properties of the MBL phase, both in experiments and numerical simulations. We demonstrate the latter by numerically constructing an extensive set of LIOMs in the MBL phase of a disordered spin chain model. We show that the resulting LIOMs are quasi-local, and use their decay to extract the localization length and establish the location of the transition between the MBL and ergodic phases.

cond-mat.dis-nn↗

arXiv2014

Eigenstate Thermalization and Representative States on Subsystems

We consider a quantum system A U B made up of degrees of freedom that can be partitioned into spatially disjoint regions A and B. When the full system is in a pure state in which regions A and B are entangled, the quantum mechanics of region A described without reference to its complement is traditionally assumed to require a reduced density matrix on A. While this is certainly true as an exact matter, we argue that under many interesting circumstances expectation values of typical operators anywhere inside A can be computed from a suitable pure state on A alone, with a controlled error. We use insights from quantum statistical mechanics - specifically the eigenstate thermalization hypothesis (ETH) - to argue for the existence of such "representative states".

cond-mat.stat-mech↗