arXiv subjects

Claudio Chamon

Publications and source records attributed to Claudio Chamon.

At least 55 records · Page 3Linked to original sources

arXiv2020

Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

We introduce the notion of combinatorial gauge symmetry -- a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states) -- that preserve the commutation and anti-commutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated to the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.

cond-mat.str-el↗

arXiv2020

Landau Theory for Non-Equilibrium Steady States

We examine how systems in non-equilibrium steady states close to a continuous phase transition can still be described by a Landau potential if one forgoes the assumption of analyticity. In a system simultaneously coupled to several baths at different temperatures, the non-analytic potential arises from the different density of states of the baths. In periodically driven-dissipative systems, the role of multiple baths is played by a single bath transferring energy at different harmonics of the driving frequency. The mean-field critical exponents become dependent on the low-energy features of the two most singular baths. We propose an extension beyond mean field.

cond-mat.stat-mech↗

arXiv2019

Fast counting with tensor networks

We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.

cond-mat.stat-mech↗

arXiv2019

Catastrophe theory classification of Fermi surface topological transitions in two dimensions

We classify all possible singularities in the electronic dispersion of two-dimensional systems that occur when the Fermi surface changes topology, using catastrophe theory. For systems with up to seven control parameters (i.e., pressure, strain, bias voltage, etc), the theory guarantees that the singularity belongs to to one of seventeen standard types. We show that at each of these singularities the density of states diverges as a power law, with a universal exponent characteristic of the particular catastrophe, and we provide its universal ratio of amplitudes of the prefactors of energies above and below the singularity. We further show that crystal symmetry restricts which types of catastrophes can occur at the points of high symmetry in the Brillouin zone. For each of the seventeen wallpaper groups in two-dimensions, we list which catastrophes are possible at each high symmetry point.

cond-mat.str-el↗

arXiv2019

Multicritical Fermi surface topological transitions

A wide variety of complex phases in quantum materials are driven by electron-electron interactions, which are enhanced through density of states peaks. A well known example occurs at van Hove singularities where the Fermi surface undergoes a topological transition. Here we show that higher order singularities, where multiple disconnected leaves of Fermi surface touch all at once, naturally occur at points of high symmetry in the Brillouin zone. Such multicritical singularities can lead to stronger divergences in the density of states than canonical van Hove singularities, and critically boost the formation of complex quantum phases via interactions. As a concrete example of the power of these Fermi surface topological transitions, we demonstrate how they can be used in the analysis of experimental data on Sr$_3$Ru$_2$O$_7$. Understanding the related mechanisms opens up new avenues in material design of complex quantum phases.

cond-mat.str-el↗

arXiv2019

Obstacles to quantum annealing in a planar embedding of XORSAT

We introduce a planar embedding of the k-regular k-XORSAT problem, in which solutions are encoded in the ground state of a classical statistical mechanics model of reversible logic gates arranged on a square grid and acting on bits that represent the Boolean variables of the problem. The special feature of this embedding is that the resulting model lacks a finite-temperature phase transition, thus bypassing the first-order thermodynamic transition known to occur in the random graph representation of XORSAT. In spite of this attractive feature, the thermal relaxation into the ground state displays remarkably slow glassy behavior. The question addressed in this paper is whether this planar embedding can afford an efficient path to solution of k-regular k-XORSAT via quantum adiabatic annealing. We first show that our model bypasses an avoided level crossing and consequent exponentially small gap in the limit of small transverse fields. We then present quantum Monte Carlo results for our embedding of the k-regular k-XORSAT that strongly support a picture in which second-order and first-order transitions develop at a finite transverse field for k = 2 and k = 3, respectively. This translates into power-law and exponential dependences in the scaling of energy gaps with system size, corresponding to times-to-solution which are, respectively, polynomial and exponential in the number of variables. We conclude that neither classical nor quantum annealing can efficiently solve our reformulation of XORSAT, even though the original problem can be solved in polynomial time by Gaussian elimination.

cond-mat.stat-mech↗

arXiv2019

Braiding photonic topological zero modes

A remarkable property of quantum mechanics in two-dimensional (2D) space is its ability to support "anyons," particles that are neither fermions nor bosons. Theory predicts that these exotic excitations can be realized as bound states confined near topological defects, like Majorana zero modes trapped in vortices in topological superconductors. Intriguingly, in the simplest cases the nontrivial phase that arises when such defects are "braided" around one another is not intrinsically quantum mechanical; rather, it can be viewed as a manifestation of the geometric (Pancharatnam-Berry) phase in wave mechanics, enabling the simulation of such phenomena in classical systems. Here we report the first experimental measurement in any system, quantum or classical, of the geometric phase due to such a braiding process. These measurements are obtained using an interferometer constructed from highly tunable 2D arrays of photonic waveguides. Our results introduce photonic lattices as a versatile playground for the experimental study of topological defects and their braiding, complementing ongoing efforts in solid-state systems and cold atomic gases.

physics.optics↗

arXiv2019

Ground state degeneracy of non-Abelian topological phases from coupled wires

We construct a family of two-dimensional non-Abelian topological phases from coupled wires using a non-Abelian bosonization approach. We then demonstrate how to determine the nature of the non-Abelian topological order (in particular, the anyonic excitations and the topological degeneracy on the torus) realized in the resulting gapped phases of matter. This paper focuses on the detailed case study of a coupled-wire realization of the bosonic $su(2)^{\,}_{2}$ Moore-Read state, but the approach we outline here can be extended to general bosonic $su(2)^{\,}_{k}$ topological phases described by non-Abelian Chern-Simons theories. We also discuss possible generalizations of this approach to the construction of three-dimensional non-Abelian topological phases.

cond-mat.str-el↗

arXiv2019

Hierarchical Majoranas in a Programmable Nanowire Network

We propose a hierarchical architecture for building "logical" Majorana zero modes using "physical" Majorana zero modes at the Y-junctions of a hexagonal network of semiconductor nanowires. Each Y-junction contains three "physical" Majoranas, which hybridize when placed in close proximity, yielding a single effective Majorana mode near zero energy. The hybridization of effective Majorana modes on neighboring Y-junctions is controlled by applied gate voltages on the links of the honeycomb network. This gives rise to a tunable tight-binding model of effective Majorana modes. We show that selecting the gate voltages that generate a Kekulé vortex pattern in the set of hybridization amplitudes yields an emergent "logical" Majorana zero mode bound to the vortex core. The position of a logical Majorana can be tuned adiabatically, \textit{without} moving any of the "physical" Majoranas or closing any energy gaps, by programming the values of the gate voltages to change as functions of time. A nanowire network supporting multiple such "logical" Majorana zero modes provides a physical platform for performing adiabatic non-Abelian braiding operations in a fully controllable manner.

cond-mat.mes-hall↗

arXiv2019

Quantum oscillations and criticality in a fermionic and bosonic dimer model for the cuprates

We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. Based on gauge invariance, we argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets touch pairwise in the interior of the Brillouin zone. The same van Hove singularity leads to a maximum in the d-wave superconducting pairing amplitude when anti-ferromagnetic interactions are included. Our combined results therefore suggest that a quantum critical point separating the underdoped and overdoped regimes is marked by the location of the van Hove saddle point in the fermionic dimer dispersion.

cond-mat.str-el↗

arXiv2019

Topological many-body scar states in dimensions 1, 2, and 3

We propose an exact construction for atypical excited states of a class of non-integrable quantum many-body Hamiltonians in one dimension (1D), two dimensions (2D), and three dimensins (3D) that display area law entanglement entropy. These examples of many-body `scar' states have, by design, other properties, such as topological degeneracies, usually associated with the gapped ground states of symmetry protected topological phases or topologically ordered phases of matter.

cond-mat.other↗

arXiv2018

Ultra-slow dynamics in a translationally invariant spin model for multiplication and factorization

We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We prove that, for open boundary conditions, the model exhibits no finite-temperature phase transition. Yet we find that it displays glassy dynamics with astronomically slow relaxation times, numerically consistent with a double exponential dependence on the inverse temperature. The slowness of the dynamics arises due to errors that occur during thermal annealing that cost little energy but flip an extensive number of spins. We argue that the energy barrier that needs to be overcome in order to heal such defects scales linearly with the correlation length, which diverges exponentially with inverse temperature, thus yielding the double exponential behavior of the relaxation time.

cond-mat.stat-mech↗

arXiv2018

Scrambling via Braiding of Nonabelions

We study how quantum states are scrambled via braiding in systems of non-Abelian anyons through the lens of entanglement spectrum statistics. In particular, we focus on the degree of scrambling, defined as the randomness produced by braiding, at the same amount of entanglement entropy. To quantify the degree of randomness, we define a distance between the entanglement spectrum level spacing distribution of a state evolved under random braids and that of a Haar-random state, using the Kullback-Leibler divergence $D_{\mathrm{KL}}$. We study $D_{\mathrm{KL}}$ numerically for random braids of Majorana fermions (supplemented with random local four-body interactions) and Fibonacci anyons. For comparison, we also obtain $D_{\mathrm{KL}}$ for the Sachdev-Ye-Kitaev model of Majorana fermions with all-to-all interactions, random unitary circuits built out of (a) Hadamard (H), $π/8$ (T), and CNOT gates, and (b) random unitary circuits built out of two-qubit Haar-random unitaries. To compare the degree of randomness that different systems produce beyond entanglement entropy, we look at $D_{\mathrm{KL}}$ as a function of the Page limit-normalized entanglement entropy $S/S_{\mathrm{max}}$. Our results reveal a hierarchy of scrambling among various models --- even for the same amount of entanglement entropy --- at intermediate times, whereas all models exhibit the same late-time behavior. In particular, we find that braiding of Fibonacci anyons randomizes initial product states more efficiently than the universal H+T+CNOT set.

cond-mat.str-el↗

arXiv2018

Steady-state superconductivity in electronic materials with repulsive interactions

We study the effect of laser driving on a minimal model for a hexagonal two-dimensional material with broken inversion symmetry. Through the application of circularly polarised light and coupling to a thermal free electron bath, the system is driven into a nonequilibrium steady state with asymmetric, nonthermal carrier populations in the two valleys. We show that, in this steady state, interband superconducting correlations between electrons can develop independent of the sign of the electron-electron interactions. We discuss how our results apply, for example, to transition metal dichalcogenides. This work opens the door to technological applications of superconductivity in a range of materials that were hitherto precluded from it.

cond-mat.str-el↗

arXiv2018

Model of spin liquids with and without time-reversal symmetry

We study a model in (2+1)-dimensional spacetime that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1+1)-dimensional spacetime, coupled via current-current interactions. The model is shown to have a lattice realization in an array of two-leg quantum spin-1/2 ladders. We study the model both in the presence and absence of time-reversal symmetry, within a mean-field approximation. We find regimes in coupling space where Abelian and non-Abelian spin liquid phases are stable. In the case when the Hamiltonian is time-reversal symmetric, we find regimes where gapped Abelian and non-Abelian chiral phases appear as a result of spontaneous breaking of time-reversal symmetry. These gapped phases are separated by a discontinuous phase transition. More interestingly, we find a regime where a non-chiral gapless non-Abelian spin liquid is stable. The excitations in this regime are described by relativistic Majorana fields in (2+1)-dimensional spacetime, much as those appearing in the Kitaev honeycomb model, but here emerging in a model of coupled spin ladders that does not break SU(2) spin-rotation symmetry.

cond-mat.str-el↗

arXiv2018

Topological electronic properties of silicon

The central role that materials play in human history is exemplified by the three-age division of prehistory into the stone, bronze, and iron ages. References to our present time as the information age or silicon age epitomizes the important role that this semiconducting material came to play in the development of computers and devices that permeate our daily lives. Here we show that the electronic states in silicon have nontrivial topological structures that are captured by a network of Berry flux lines that link at points of high symmetry in the Brillouin zone. This complex network has ice-nodal points where fluxes satisfy ice rules, making silicon a "nodal-chain insulator". Fixing the longitudinal momentum parallel to such flux lines yields a two-dimensional Dirac Hamiltonian for the transverse degrees of freedom. This complex Berry-flux network implies a topologically stable two-fold degeneracy along the X-W direction in all of silicon bands, a fact that is supported by crystal symmetry arguments as well as direct inspection of the vast literature on silicon band structures. Similarly to nodal-chain semimetals, we find drumhead-like states in the regions that are delimited by the projections of the bulk Berry flux network on the surface Brillouin zone.

cond-mat.mes-hall↗

arXiv2018

Tensor network method for reversible classical computation

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs/outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

cond-mat.stat-mech↗

arXiv2018

Dynamic scaling of topological ordering in classical systems

We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional $\mathbb{Z}_2$ (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a non-local order parameter (defined using Wilson loops) and a dynamic exponent $z=2.70 \pm 0.03$, the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature---the Ising chain, the two-dimensional $\mathbb{Z}_2$ gauge model, and a three-dimensional star model (another variant of the $\mathbb{Z}_2$ gauge model). In these systems the correlation length diverges exponentially, in a way that is non-smooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface.

cond-mat.stat-mech↗