arXiv subjects

Nicolas Macé

Publications and source records attributed to Nicolas Macé.

15 recordsLinked to original sources

arXiv2025

Safe Pareto Improvements for Expected Utility Maximizers in Program Games

Agents in mixed-motive coordination problems such as Chicken may fail to coordinate on a Pareto-efficient outcome. Safe Pareto improvements (SPIs) were originally proposed to mitigate miscoordination in cases where players lack probabilistic beliefs as to how their delegates will play a game; delegates are instructed to behave so as to guarantee a Pareto improvement on how they would play by default. More generally, SPIs may be defined as transformations of strategy profiles such that all players are necessarily better off under the transformed profile. In this work, we investigate the extent to which SPIs can reduce downsides of miscoordination between expected utility-maximizing agents. We consider games in which players submit computer programs that can condition their decisions on each other's code, and use this property to construct SPIs using programs capable of renegotiation. We first show that under mild conditions on players' beliefs, each player always prefers to use renegotiation. Next, we show that under similar assumptions, each player always prefers to be willing to renegotiate at least to the point at which they receive the lowest payoff they can attain in any efficient outcome. Thus subjectively optimal play guarantees players at least these payoffs, without the need for coordination on specific Pareto improvements. Lastly, we prove that renegotiation does not guarantee players any improvements on this bound.

cs.GT↗

arXiv2023

Evolutionary Stability of Other-Regarding Preferences Under Complexity Costs

The evolution of preferences that account for other agents' fitness, or other-regarding preferences, has been modeled with the "indirect approach" to evolutionary game theory. Under the indirect evolutionary approach, agents make decisions by optimizing a subjective utility function. Evolution may select for subjective preferences that differ from the fitness function, and in particular, subjective preferences for increasing or reducing other agents' fitness. However, indirect evolutionary models typically artificially restrict the space of strategies that agents might use (assuming that agents always play a Nash equilibrium under their subjective preferences), and dropping this restriction can undermine the finding that other-regarding preferences are selected for. Can the indirect evolutionary approach still be used to explain the apparent existence of other-regarding preferences, like altruism, in humans? We argue that it can, by accounting for the costs associated with the complexity of strategies, giving (to our knowledge) the first account of the relationship between strategy complexity and the evolution of preferences. Our model formalizes the intuition that agents face tradeoffs between the cognitive costs of strategies and how well they interpolate across contexts. For a single game, these complexity costs lead to selection for a simple fixed-action strategy, but across games, when there is a sufficiently large cost to a strategy's number of context-specific parameters, a strategy of maximizing subjective (other-regarding) utility is stable again. Overall, our analysis provides a more nuanced picture of when other-regarding preferences will evolve.

cs.GT↗

arXiv2022

Superfluidity vs prethermalisation in a nonlinear Floquet system

We show that superfluidity can be used to prevent thermalisation in a nonlinear Floquet system. Generically, periodic driving boils an interacting system to a featureless infinite temperature state. Fast driving is a known strategy to postpone Floquet heating with a large but always finite boiling time. In contrast, using a nonlinear periodically-driven system on a lattice, we show the existence of a continuous class of initial states which do not thermalise at all. This absence of thermalisation is associated to the existence and persistence of a stable superflow motion.

cond-mat.quant-gas↗

arXiv2022

Topological order in random interacting Ising-Majorana chains stabilized by many-body localization

We numerically explore $\mathbb Z_2$-symmetric random interacting Ising-Majorana chains at high energy. A very rich phase diagram emerges with two topologically distinct many-body localization (MBL) regimes separated by a much broader thermal phase than previously found. This is a striking consequence of the avalanche theory. We further find MBL spin-glass order always associated to a many-body spectral pairing, presumably signaling a strong zero mode operator which opens fascinating perspectives for MBL-protected topological qubits.

cond-mat.dis-nn↗

arXiv2022

Probing symmetries of quantum many-body systems through gap ratio statistics

The statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of random matrices and Poisson statistics. In this work we extend the study of the gap ratio distribution P(r) to the case where discrete symmetries are present. This is important, since in certain situations it may be very impractical, or impossible, to split the model into symmetry sectors, let alone in cases where the symmetry is not known in the first place. Starting from the known expressions for surmises in the Gaussian ensembles, we derive analytical surmises for random matrices comprised of several independent blocks. We check our formulae against simulations from large random matrices, showing excellent agreement. We then present a large set of applications in many-body physics, ranging from quantum clock models and anyonic chains to periodically-driven spin systems. In all these models the existence of a (sometimes hidden) symmetry can be diagnosed through the study of the spectral gap ratios, and our approach furnishes an efficient way to characterize the number and size of independent symmetry subspaces. We finally discuss the relevance of our analysis for existing results in the literature, as well as its practical usefulness, and point out possible future applications and extensions.

cond-mat.dis-nn↗

arXiv2020

Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain

Despite tremendous theoretical efforts to understand subtleties of the many-body localization (MBL) transition, many questions remain open, in particular concerning its critical properties. Here we make the key observation that MBL in one dimension is accompanied by a spin freezing mechanism which causes chain breakings in the thermodynamic limit. Using analytical and numerical approaches, we show that such chain breakings directly probe the typical localization length, and that their scaling properties at the MBL transition agree with the Kosterlitz-Thouless scenario predicted by phenomenological renormalization group approaches.

cond-mat.dis-nn↗

arXiv2019

Quantum circuit at criticality

We study a simple quantum circuit model which, without need for fine tuning, is very close to sitting at the transition between ergodic and many-body localized (MBL) phases. We probe the properties of the model on large finite-size systems, using a matrix-free exact diagonalization method that takes advantage of the shallow nature of the circuit. Moreover, we provide a qualitative entanglement bottleneck picture to account for the close-to-critical nature of the model.

cond-mat.dis-nn↗

arXiv2019

Multifractal Scalings across the Many-Body Localization Transition

In contrast with Anderson localization where a genuine localization is observed in real space, the many-body localization (MBL) problem is much less understood in the Hilbert space, support of the eigenstates. In this work, using exact diagonalization techniques we address the ergodicity properties in the underlying ${\cal{N}}$-dimensional complex networks spanned by various computational bases for up to $L=24$ spin-1/2 particles (i.e. Hilbert space of size ${\cal{N}}\simeq 2.7\,10^6$). We report fully ergodic eigenstates in the delocalized phase (irrespective of the computational basis), while the MBL regime features a generically (basis-dependent) multifractal behavior, delocalized but non-ergodic. The MBL transition is signaled by a non-universal jump of the multifractal dimensions.

cond-mat.dis-nn↗

arXiv2019

From eigenstate to Hamiltonian: Prospects for ergodicity and localization

This paper addresses the so-called inverse problem which consists in searching for (possibly multiple) parent target Hamiltonian(s), given a single quantum state as input. Starting from $Ψ_0$, an eigenstate of a given local Hamiltonian $\mathcal{H}_0$, we ask whether or not there exists another parent Hamiltonian $\mathcal{H}_\mathrm{P}$ for $Ψ_0$, with the same local form as $\mathcal{H}_0$. Focusing on one-dimensional quantum disordered systems, we extend the recent results obtained for Bose-glass ground states [M. Dupont and N. Laflorencie, Phys. Rev. B 99, 020202(R) (2019)] to Anderson localization, and the many-body localization (MBL) physics occurring at high energy. We generically find that any localized eigenstate is a very good approximation for an eigenstate of a distinct parent Hamiltonian, with an energy variance $σ_\mathrm{P}^2(L)=\langle\mathcal{H}_\mathrm{P}^2\rangle_{Ψ_0}-\langle\mathcal{H}_\mathrm{P}\rangle_{Ψ_0}^2$ vanishing as a power law of system size $L$. This decay is microscopically related to a chain-breaking mechanism, also signalled by bottlenecks of vanishing entanglement entropy. A similar phenomenology is observed for both Anderson and MBL. In contrast, delocalized ergodic many-body eigenstates uniquely encode the Hamiltonian in the sense that $σ_\mathrm{P}^2(L)$ remains finite at the thermodynamic limit, i.e., $L\to+\infty$. As a direct consequence, the ergodic-MBL transition can be very well captured from the scaling of $σ_\mathrm{P}^2(L)$.

cond-mat.dis-nn↗

arXiv2019

Many-body localization in a quasiperiodic Fibonacci chain

We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential values. Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.

cond-mat.dis-nn↗

arXiv2018

Shift-invert diagonalization of large many-body localizing spin chains

We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl/. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to $L=26$. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.

cond-mat.dis-nn↗

arXiv2017

Critical eigenstates and their properties in one and two dimensional quasicrystals

We present exact solutions for some eigenstates of hopping models on one and two dimensional quasiperiodic tilings and show that they are "critical" states, by explicitly computing their multifractal spectra. These eigenstates are shown to be generically present in 1D quasiperiodic chains, of which the Fibonacci chain is a special case. We then describe properties of the ground states for a class of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker tilings. Exact and numerical solutions are seen to be in good agreement.

cond-mat.dis-nn↗

arXiv2017

Gap structure of 1D cut and project Hamiltonians

We study the gap properties of nearest neighbors tight binding models on quasiperiodic chains. We argue that two kind of gaps should be distinguished: stable and transient. We show that stable gaps have a well defined quasiperiodic limit. We also show that there is a direct relation between the gap size and the gap label.

cond-mat.dis-nn↗

arXiv2016

Quantum simulation of a 2D quasicrystal with cold atoms

We describe a way to obtain a two-dimensional quasiperiodic tiling with eight-fold symmetry using cold atoms. A series of such optical tilings, related by scale transformations, is obtained for a series of specific values of the chemical potential of the atoms. A theoretical model for the optical system is described and compared with that of the well-known cut-and-project method for the Ammann-Beenker tiling. This type of cold atom structure should allow the simulation of several important lattice models for interacting quantum particles and spins in quasicrystals.

cond-mat.quant-gas↗

arXiv2016

Fractal dimensions of the wavefunctions and local spectral measures on the Fibonacci chain

We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a new symmetry of wavefunctions under permutation of site and energy indices. We compute the wavefunction renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wavefunctions, as well as their global averages. The multifractality of wavefunctions is seen to appear at next-to-leading order in the ratio of the hopping amplitudes, $ρ$. Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of $ρ$ well outside the domain of applicability of perturbation theory.

cond-mat.mes-hall↗