The question whether Anderson insulators can persist to finite-strength interactions-a scenario dubbed many-body localization-has recently received a great deal of interest. The origin of such a ...many-body localized phase has been described as localization in Fock space, a picture we examine numerically. We then formulate a precise sense in which a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator. We call such a state a many-body localized state and define a many-body localized phase as one in which almost all states are many-body localized states. We explore the possible consequences of this; the most striking is an area law for the entanglement entropy of almost all excited states in a many-body localized phase. We present the results of numerical calculations for a one-dimensional system of spinless fermions. Our results are consistent with an area law and, by implication, many-body localization for almost all states and almost all regions for weak enough interactions and strong disorder. However, there are rare regions and rare states with much larger entanglement entropies. Furthermore, we study the implications that many-body localization may have for topological phases and self-correcting quantum memories. We find that there are scenarios in which many-body localization can help to stabilize topological order at non-zero energy density, and we propose potentially useful criteria to confirm these scenarios.
Classical discrete time crystals Yao, Norman Y.; Nayak, Chetan; Balents, Leon ...
Nature physics,
04/2020, Letnik:
16, Številka:
4
Journal Article
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The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective ...subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially long timescales. Power-law correlations are present along a first-order line, which terminates at a critical point. We analyse the transition by mapping it to the locked-to-sliding transition of a d.c.-driven charge density wave. Finally, building upon results from the field of probabilistic cellular automata, we conjecture the existence of classical time crystals with true long-range order, where time-translation symmetry is broken out to infinite times.The phenomenon of many-body localization gives rise to entirely new phases of quantum matter when it is driven away from equilibrium. A numerical study now shows that one of these phases—the discrete time crystal—can also occur in a classical spin chain.
We provide a current perspective on the rapidly developing field of Majorana zero modes (MZMs) in solid-state systems. We emphasise the theoretical prediction, experimental realisation and potential ...use of MZMs in future information processing devices through braiding-based topological quantum computation (TQC). Well-separated MZMs should manifest non-Abelian braiding statistics suitable for unitary gate operations for TQC. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localised at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic MZMs in solid-state systems. We also discuss fractional quantum Hall systems (the 5/2 state), which have been extensively studied in the context of non-Abelian anyons and TQC. We describe proposed schemes for carrying out braiding with MZMs as well as the necessary steps for implementing TQC.
In a periodically driven (Floquet) system, there is the possibility for new phases of matter, not present in stationary systems, protected by discrete time-translation symmetry. This includes ...topological phases protected in part by time-translation symmetry, as well as phases distinguished by the spontaneous breaking of this symmetry, dubbed “Floquet time crystals.” We show that such phases of matter can exist in the prethermal regime of periodically driven systems, which exists generically for sufficiently large drive frequency, thereby eliminating the need for integrability or strong quenched disorder, which limited previous constructions. We prove a theorem that states that such a prethermal regime persists until times that are nearly exponentially long in the ratio of certain couplings to the drive frequency. By similar techniques, we can also construct stationary systems that spontaneously break continuous time-translation symmetry. Furthermore, we argue that for driven systems coupled to a cold bath, the prethermal regime could potentially persist to infinite time.
Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems ...is those that do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new nonequilibrium phases of matter. In particular, we focus on discrete time crystals, which are many-body phases of matter characterized by a spontaneously broken discrete time-translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a nonequilibrium phenomenon that is stabilized by many-body interactions, with no analog in noninteracting systems. We explain the theory behind several proposed models of discrete time crystals, and compare several recent realizations, in different experimental contexts.
Quantum computation by non-Abelian Majorana zero modes (MZMs) offers an approach to achieve fault tolerance by encoding quantum information in the non-local charge parity states of semiconductor ...nanowire networks in the topological superconductor regime. Thus far, experimental studies of MZMs chiefly relied on single electron tunneling measurements, which lead to the decoherence of the quantum information stored in the MZM. As a next step towards topological quantum computation, charge parity conserving experiments based on the Josephson effect are required, which can also help exclude suggested non-topological origins of the zero bias conductance anomaly. Here we report the direct measurement of the Josephson radiation frequency in indium arsenide nanowires with epitaxial aluminium shells. We observe the 4π-periodic Josephson effect above a magnetic field of ≈200 mT, consistent with the estimated and measured topological phase transition of similar devices.
We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of ...quantum state teleportation, we show how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.
•Using MRI compatible EEG reduces non-monitored time for patients in the critical care unit.•MRI compatible EEG electrodes do not interfere with the quality of MRI scans.•Using MRI Compatible EEG is ...cost-effective because it needs a single hookup and reduces burden for the EEG technician.
Continuous video-EEG (cvEEG) monitoring is a vastly utilized tool for monitoring critically ill patients in the intensive care unit. Our study investigates the clinical utility and cost-effectiveness of using MRI Compatible EEG electrode system for patients being monitored in the intensive care unit.
This retrospective study included 14 critically ill patients who underwent cvEEG between March 2019 to March 2020. They were classified into 2 subgroups: Group 1- ‘MRI-compatible EEG’ (mean age: 56.00 ± 19.99 years; M:F = 2:5; N = 7), Group 2 – ‘Conventional EEG’ (mean age: 49.14 ± 24.76 years; M:F = 4:3; N = 7). The EEG monitoring times as well as cost-effectiveness of cvEEG between the groups were compared using Mann-Whitney Test (p ≤ 0.05). We also compared the MRI quality between the groups using Chi-squared test (p ≤ 0.05).
The EEG non-monitored time in Group 2 (7.62 ± 6.45 h) was significantly higher than Group 1 (2.71 ± 2.34 h) (p = 0.025). The average daily cost for cvEEG in Group 1 ($2098.53 ± 493.58) and Group 2 ($2230.58 ± 142.73) was comparable (p = 0.896). The quality of MRI scans between Group 1 (6/7) and 2 (6/7) were also comparable (p = 1.000).
The monitoring time lost in patients with MRI Compatible EEG electrodes was significantly lower than the patients with Conventional EEG electrodes. The daily cost of monitoring and the quality of MRI scans were comparable between the 2 groups. We conclude that the use of MRI Compatible EEG electrodes is a practical and cost-effective method to improve the quality of monitoring in critically ill patients.
A 3D fermionic topological insulator has a gapless Dirac surface state protected by time-reversal symmetry and charge conservation symmetry. The surface state can be gapped by introducing ...ferromagnetism to break time-reversal symmetry, introducing superconductivity to break charge conservation, or entering a topological phase. In this paper, we construct a minimal gapped topological phase that preserves both time-reversal and charge conservation symmetries and supports Ising-type non-Abelian anyons. This phase can be understood heuristically as emerging from a surface s-wave superconducting state via the condensation of eight-vortex composites. The topological phase inherits vortices supporting Majorana zero modes from the surface superconducting state. However, since it is time-reversal invariant, the surface topological phase is a distinct phase from the Ising topological phase, which can be viewed as a quantum-disordered spin-polarized px + ipy superconductor. We discuss the anyon model of this topological phase and the manner in which time-reversal symmetry is realized in it. We also study the interfaces between the topological state and other surface gapped phases.
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