Abstracts > Tuesday 14

Abstract. Experiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this talk, I will discuss this problem presenting the data from a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer and recently published [Communications Physics 4 (2021) 74]. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length \(\xi\) ;. Indeed, an emerging length-scale \(\xi^\star\) rules the crossover from weak (at \(\xi\ll \xi^\star\)) to strong chaos (\(\xi\gg \xi^\star\)). Extrapolations of \(\xi^\star\) to relevant experimental conditions are provided.

Abstract. Bidimensional solid phases have quasi long-range translational order and keep long-range orientational order. In the standard picture melting is driven by the unbinding of topological defects and follows two steps: an intermediate phase with quasi long-range orientational order is reached by the unbinding of dislocations while the transition to the liquid is triggered by the unbinding of disclinations. In this talk I will revisit these mechanisms and I will extend their analysis to systems of self- propelled particles.

Abstract. A central tenant in the classification of phases is that boundary conditions cannot affect the bulk properties of a system. We present striking, yet puzzling, evidence of a clear violation of this assumption. We consider spin chains (with no external field) in a ring geometry with an odd number of sites (a setting we term Frustrated Boundary Conditions, FBC) and both ferromagnetic and antiferromagnetic interactions. In such a setting, even at finite sizes, we are able to calculate directly the order parameters (namely, the spontaneous magnetizations). When ferromagnetic interactions dominate, we recover the expected behavior, but when the system is governed by one AFM interaction, the magnetizations decay algebraically to zero with the system size (while not being staggered). With two competing AFM interactions a third, new type of order emerges, with a magnetization profile that varies in space with an incommensurate pattern. This modulation is the result of a ground state degeneracy which leads to a breaking of translational invariance. The transition between the two latter cases is a first order boundary QPT, which exists only with a suitable choice of boundary conditions (FBC). In other models, the order and disorder parameters across a second order QPT are destroyed and replaced by string order parameters, thus changing the nature of a QPT by boundary conditions. Finally, we consider a dynamical setting and show how the Loschmidt echo clearly distinguishes the parity in the number of sites of a spin chain for arbitrarily large systems.

Abstract. In this work inhomogeneous quantum quenches are studied in the attractive regime of the sine-Gordon model. In the quench protocol under investigation, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine-Gordon Hamiltonian. Varying either the interaction strength of the sine-Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein-Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine-Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine-Gordon dynamics in arbitrary inhomogeneous settings.

Abstract. The comparison of performance between quantum walks and classical walks on graphs has been used recently as a tool for studying quantum advantage. A few graph families have been suggested in which a quantum walker can get through a graph exponentially faster than a classical walker, which led to the development of a family of stoquastic-Hamiltonian problems for which a quantum computer is sub-exponentially advantageous over a classical one. However, the examples mentioned above are extremely sensitive to disorder in the graph: With weak disorder, the quantum walker is led to diffusive dynamics, in which it behaves like a classical walker. And even worse, strong disorder leads to localization, which prevents the quantum walker from moving through the graph, as opposed to a classical walker, which remains diffusive. What can we learn from the behavior of quantum walks on disordered graphs? In this work, we combine quantum information tools with the study of Anderson localization phenomena in order to obtain a complexity bound on the localization-phase-transition critical exponent.

Abstract. The Landauer principle states that at least \(k_BT\ln 2\) of energy is required to erase a 1-bit memory, with \(k_B T\) the thermal energy of the system. Practical erasures implementations require overhead to the Landauer’s bound, observed to scale as \(k_B T × B/\tau\), with \(\tau\) the protocol duration and \(B\) close to the system relaxation time. Most experiments use overdamped systems, for which minimizing the overhead means minimizing the dissipation. Underdamped systems thus sounds appealing to reduce this energetic cost. We study the effects of inertia on this bound using as one-bit memory an underdamped micro-mechanical oscillator confined in a double-well potential created by a feedback loop. The potential barrier is precisely tunable in the few \(k_B T\) range. We measure, within the stochastic thermodynamic framework, the work and the heat of the erasure protocol. We demonstrate experimentally and theoretically that, in this underdamped system, the Landauer bound is reached with a 1 with protocols as short as 100 ms. Besides, we show experimentally and theoretically that for such underdamped systems, fast erasures induce heating of the memory: the work influx is not instantaneously compensated by the inefficient heat transfer to the thermostat. This temperature rise results in a kinetic and potential energy contribution superseding the viscous dissipation term. Our model covering all damping regimes paves the way to new optimisation strategies in information processing, based on the thorough understanding of the energy exchanges. Encouraged by the success of using an underdamped system to study stochastic thermodynamics, we are now using a FPGA (Field-Programmable Gate Arrays ) to implement complex feedback operations. The resulting virtual potential can be shaped arbitrarily with high precision and can follow elaborate procedures. This tool opens a wide panel of possible future experiments.