arXiv subjects

A. Scardicchio

Publications and source records attributed to A. Scardicchio.

At least 19 recordsLinked to original sources

arXiv2026

On the Optimal Layout of Two-Dimensional Lattices for Density Matrix Renormalization Group

For quantum spin models defined on a two-dimensional lattice, we look for the best numbering of the lattice sites (a layout) that, at fixed bond dimension and other parameters of the density matrix renormalization group (DMRG) algorithm, gives the lowest value of the variational energy, maximum entropy and truncation error. We consider the conjecture that the optimal layout is a Hamiltonian path, and that it optimizes a simply computable geometric cost function. Finding the minimum of such a function, which is a variant of the minimum linear arrangement problem, provides the DMRG with an efficient layout of the lattice and improves both accuracy and convergence time. We present applications to the antiferromagnetic and spin glass spin-1/2 models on the square and triangular lattices.

cond-mat.str-el↗

arXiv2024

Optimal control of a quantum sensor: A fast algorithm based on an analytic solution

Quantum sensors can show unprecedented sensitivities, provided they are controlled in a very specific, optimal way. Here, we consider a spin sensor of time-varying fields in the presence of dephasing noise, and we show that the problem of finding the pulsed control field that optimizes the sensitivity (i.e., the smallest detectable signal) can be mapped to the determination of the ground state of a spin chain. We find an approximate but analytic solution of this problem, which provides a \emph{lower bound} for the sensitivity and a pulsed control very close to optimal, which we further use as initial guess for realizing a fast simulated annealing algorithm. We experimentally demonstrate the sensitivity improvement for a spin-qubit magnetometer based on a nitrogen-vacancy center in diamond.

quant-ph↗

arXiv2019

Non-Abelian symmetries and disorder: a broad non-ergodic regime and anomalous thermalization

Symmetries play a central role in single-particle localization. Recent research focused on many-body localized (MBL) systems, characterized by new kind of integrability, and by the area-law entanglement of eigenstates. We investigate the effect of a non-Abelian $SU(2)$ symmetry on the dynamical properties of a disordered Heisenberg chain. While $SU(2)$ symmetry is inconsistent with the conventional MBL, a new non-ergodic regime is possible. In this regime, the eigenstates exhibit faster than area-law, but still a strongly sub-thermal scaling of entanglement entropy. Using exact diagonalization, we establish that this non-ergodic regime is indeed realized in the strongly disordered Heisenberg chains. We use real-space renormalization group (RSRG) to construct approximate excited eigenstates, and show their accuracy for systems of size up to $L=26$. As disorder strength is decreased, a crossover to the thermalizing phase occurs. To establish the ultimate fate of the non-ergodic regime in the thermodynamic limit, we develop a novel approach for describing many-body processes that are usually neglected by RSRG, accessing systems of size $L>2000$. We characterize the resonances that arise due to such processes, finding that they involve an ever growing number of spins as the system size is increased. The probability of finding resonances grows with the system size. Even at strong disorder, we can identify a large lengthscale beyond which resonances proliferate. Presumably, this eventually would drive the system to a thermalizing phase. However, the extremely long thermalization time scales indicate that a broad non-ergodic regime will be observable experimentally. Our study demonstrates that symmetries control dynamical properties of disordered, many-body systems. The approach introduced here provides a versatile tool for describing a broad range of disordered many-body systems.

cond-mat.str-el↗

arXiv2017

Clustering of non-ergodic eigenstates in quantum spin glasses

The two primary categories for eigenstate phases of matter at finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that in the paradigmatic quantum $p$-spin models of spin-glass theory, eigenstates violate ETH yet are not MBL either. A mobility edge, which we locate to leading order in $1/p$ using the forward-scattering approximation and replica techniques, separates the non-ergodic phase at small transverse field from an ergodic phase at large transverse field. The non-ergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in spin-glass theory. We show that the non-ergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.

cond-mat.dis-nn↗

arXiv2016

Review: Local Integrals of Motion in Many-Body Localized systems

We review the current (as of Fall 2016) status of the studies on the emergent integrability in many-body localized models. We start by explaining how the phenomenology of fully many-body localized systems can be recovered if one assumes the existence of a complete set of (quasi)local operators which commute with the Hamiltonian (local integrals of motion, or LIOMs). We describe the evolution of this idea from the initial conjecture, to the perturbative constructions, to the mathematical proof given for a disordered spin chain. We discuss the proposed numerical algorithms for the construction of LIOMs and the status of the debate on the existence and nature of such operators in systems with a many-body mobility edge, and in dimensions larger than one.

cond-mat.dis-nn↗

arXiv2016

Many-body localization beyond eigenstates in all dimensions

Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators (l$^*$-bits) underlie localization in such systems. In dimensions $d>1$, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to l$^*$-bits. Physical consequences of l$^*$-bits include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in $d=1$ and thermal eigenstates at all parameters in $d>1$. Near-term experiments in ultra-cold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of l$^*$-bits.

cond-mat.dis-nn↗

arXiv2015

Total correlations of the diagonal ensemble herald the many-body localization transition

The intriguing phenomenon of many-body localization (MBL) has attracted significant interest recently, but a complete characterization is still lacking. In this work, we introduce the total correlations, a concept from quantum information theory capturing multi-partite correlations, to the study of this phenomenon. We demonstrate that the total correlations of the diagonal ensemble provides a meaningful diagnostic tool to pin-down, probe, and better understand the MBL transition and ergodicity breaking in quantum systems. In particular, we show that the total correlations has sub-linear dependence on the system size in delocalized, ergodic phases, whereas we find that it scales extensively in the localized phase developing a pronounced peak at the transition. We exemplify the power of our approach by means of an exact diagonalization study of a Heisenberg spin chain in a disordered field.

cond-mat.dis-nn↗

arXiv2015

The many-body localized phase of the quantum random energy model

The random energy model (REM) provides a solvable mean-field description of the equilibrium spin glass transition. Its quantum sibling (the QREM), obtained by adding a transverse field to the REM, has similar properties and shows a spin glass phase for sufficiently small transverse field and temperature. In a recent work, some of us have shown that the QREM further exhibits a many-body localization - delocalization (MBLD) transition when viewed as a closed quantum system, evolving according to the quantum dynamics. This phase encloses the familiar equilibrium spin-glass phase. In this paper we study in detail the MBLD transition within the forward-scattering approximation and replica techniques. The predictions for the transition line are in good agreement with the exact diagonalization numerics. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.

cond-mat.stat-mech↗

arXiv2015

A large-N approximated field theory for multipartite entanglement

We study the characterization of multipartite entanglement for the random states of an $n$-qbit system. Unable to solve the problem exactly we generalize it, changing complex numbers into real vectors with $N_c$ components (the original problem is recovered for $N_c=2$). Studying the leading diagrams in the large-$N_c$ approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large-$N_c$ limit.

quant-ph↗

arXiv2015

Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices

We study a disordered classical Heisenberg magnet with uniformly antiferromagnetic interactions which are frustrated on account of their long-range Coulomb form, {\em i.e.} $J(r)\sim -A\ln r$ in $d=2$ and $J(r)\sim A/r$ in $d=3$. This arises naturally as the $T\rightarrow 0$ limit of the emergent interactions between vacancy-induced degrees of freedom in a class of diluted Coulomb spin liquids (including the classical Heisenberg antiferromagnets on checkerboard, SCGO and pyrochlore lattices) and presents a novel variant of a disordered long-range spin Hamiltonian. Using detailed analytical and numerical studies we establish that this model exhibits a very broad paramagnetic regime that extends to very large values of $A$ in both $d=2$ and $d=3$. In $d=2$, using the lattice-Green function based finite-size regularization of the Coulomb potential (which corresponds naturally to the underlying low-temperature limit of the emergent interactions between orphan-spins), we only find evidence that freezing into a glassy state occurs in the limit of strong coupling, $A=\infty$, while no such transition seems to exist at all in $d=3$. We also demonstrate the presence and importance of screening for such a magnet. We analyse the spectrum of the Euclidean random matrices describing a Gaussian version of this problem, and identify a corresponding quantum mechanical scattering problem.

cond-mat.str-el↗

arXiv2015

Localized systems coupled to small baths: from A$_{nderson}$ to Z$_{eno}$

We investigate what happens if an Anderson localized system is coupled to a small bath, with a discrete spectrum, when the coupling between system and bath is specially chosen so as to never localize the bath. We find that the effect of the bath on localization in the system is a non-monotonic function of the coupling between system and bath. At weak couplings, the bath facilitates transport by allowing the system to 'borrow' energy from the bath. But above a certain coupling the bath produces localization, because of an orthogonality catastrophe, whereby the bath 'dresses' the system and hence suppresses the hopping matrix element. We call this last regime the regime of "Zeno-localization", since the physics of this regime is akin to the quantum Zeno effect, where frequent measurements of the position of a particle impede its motion. We confirm our results by numerical exact diagonalization.

cond-mat.dis-nn↗

arXiv2015

Integrals of motion in the Many-Body localized phase

We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum $\{0,1\}$, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.

cond-mat.dis-nn↗

arXiv2014

Many-body mobility edge in a mean-field quantum spin glass

The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization - delocalization (MBLD) transition when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition using the forward-scattering approximation and replica techniques. The predictions are in good agreement with the numerics. The MBLD lies at energy density significantly above the equilibrium spin glass transition, indicating that the closed system dynamics freezes well outside of the traditional glass phase. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.

cond-mat.stat-mech↗

arXiv2014

Quantum annealing: the fastest route to quantum computation?

In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to avoided crossings inside a phase. We argue that the thermodynamic order of the phase transitions is not predictive of the scaling of the gap with the system size. On the contrary, we also argue that, if the phase surrounding the problem Hamiltonian is a Many-Body Localized (MBL) phase, the gaps are going to be typically exponentially small and that this follows naturally from the existence of local integrals of motion in the MBL phase.

quant-ph↗

arXiv2014

Anderson localization on the Bethe lattice: non-ergodicity of extended states

Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions $f(α)$ defined in Eq.(3), remains positive for $α$ noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization, i.e. the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.

cond-mat.stat-mech↗

arXiv2012

The quantum adiabatic algorithm and scaling of gaps at first order quantum phase transitions

Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum antiferromagnetic Ising chain in a staggered field can exhibit a first order transition with only an algebraically small gap. In addition, we construct a simple classical translationally invariant one-dimensional Hamiltonian containing nearest-neighbour interactions only, which exhibits an exponential gap at a thermodynamic quantum first-order transition of essentially topological origin. This establishes that (i) the QAA can be successful even across first order transitions but also that (ii) it can fail on exceedingly simple problems readily solved by inspection, or by classical annealing.

quant-ph↗

arXiv2011

Statistical distribution of the local purity in a large quantum system

The local purity of large many-body quantum systems can be studied by following a statistical mechanical approach based on a random matrix model. Restricting the analysis to the case of global pure states, this method proved to be successful and a full characterization of the statistical properties of the local purity was obtained by computing the partition function of the problem. Here we generalize these techniques to the case of global mixed states. Since the computation of the partition function is far more challenging than in the pure case, we focus on the computation of the first moments of the local purity. Finally, we establish a connection with the theory of twirling maps in quantum channels.

quant-ph↗

arXiv2010

Statistical mechanics of classical and quantum computational complexity

The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous framework for classifying the hardness of problems according to the computational resources, most notably time, needed to solve them. Its extension to quantum computers allows the relative power of quantum computers to be analyzed. This framework identifies families of problems which are likely hard for classical computers (``NP-complete'') and those which are likely hard for quantum computers (``QMA-complete'') by indirect methods. That is, they identify problems of comparable worst-case difficulty without directly determining the individual hardness of any given instance. Statistical mechanical methods can be used to complement this classification by directly extracting information about particular families of instances---typically those that involve optimization---by studying random ensembles of them. These pose unusual and interesting (quantum) statistical mechanical questions and the results shed light on the difficulty of problems for large classes of algorithms as well as providing a window on the contrast between typical and worst case complexity. In these lecture notes we present an introduction to this set of ideas with older work on classical satisfiability and recent work on quantum satisfiability as primary examples. We also touch on the connection of computational hardness with the physical notion of glassiness.

cond-mat.stat-mech↗