S. L. Sondhi

Spin Ice, Fractionalization, and Topological Order

The spin ice compounds Dy2Ti2O7 and Ho2Ti2O7 are highly unusual magnets that epitomize a set of concepts of great interest in modern condensed matter physics: Their low-energy physics exhibits an emergent gauge field and their excitations are magnetic monopoles that arise from the fractionalization of the microscopic magnetic spin degrees of freedom. In this review, we provide an elementary introduction to these concepts and we survey the thermodynamics, statics, and dynamics—in and out of equilibrium—of spin ice from these vantage points. Along the way, we touch on topics such as emergent Coulomb plasmas, observable Dirac strings, and irrational charges. We close with the outlook for these unique materials.

Order by distortion and string modes in pyrochlore antiferromagnets.

We study the effects of magnetoelastic couplings on pyrochlore antiferromagnets. We employ Landau theory, extending an investigation begun by Yamashita and Ueda for the case of S = 1, and classical analyses to argue that such couplings generate bond order via a spin-Peierls transition. This is followed by, or concurrent with, a transition into one of several possible low-temperature Néel phases, with most simply collinear, but also coplanar or mixed spin patterns. In a collinear Néel phase, a dispersionless stringlike magnon mode dominates the resulting excitation spectrum, providing a distinctive signature of the parent geometrically frustrated state. We comment on the experimental situation.

Many-body Localization and Symmetry Protected Topological Order

Recent work shows that highly excited many-body localized eigenstates can exhibit broken symmetries and topological order, including in dimensions where such order would be forbidden in equilibrium. In this paper we extend this analysis to discrete symmetry protected order via the explicit examples of the Haldane phase of one dimensional spin chains and the topological Ising paramagnet in two dimensions. We comment on the challenge of extending these results to cases where the protecting symmetry is continuous.

Kibble-Zurek problem: Universality and the scaling limit

Near a critical point, the equilibrium relaxation time of a system diverges and any change of control/thermodynamic parameters leads to non-equilibrium behavior. The Kibble-Zurek problem is to determine the dynamical evolution of the system parametrically close to its critical point when the change is parametrically slow. The non-equilibrium behavior in this limit is controlled entirely by the critical point and the details of the trajectory of the system in parameter space (the protocol) close to the critical point. Together, they define a universality class consisting of critical exponents-discussed in the seminal work by Kibble and Zurek-and scaling functions for physical quantities, which have not been discussed hitherto. In this article, we give an extended and pedagogical discussion of the universal content in the Kibble-Zurek problem. We formally define a scaling limit for physical quantities near classical and quantum transitions for different sets of protocols. We report computations of a few scaling functions in model Gaussian and large-N problems and prove their universality with respect to protocol choice. We also introduce a new protocol in which the critical point is approached asymptotically at late times with the system marginally out of equilibrium, wherein logarithmic violations to scaling and anomalous dimensions occur even in the simple Gaussian problem.

Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach.

The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.

Nonlocal adiabatic response of a localized system to local manipulations

Anderson localization has recently attracted renewed interest in strongly correlated quantum systems. Now, local adiabatic manipulations are shown to lead to a nonlocal response, with implications for quantum control in disordered environments.

Magnetization process of spin ice in a [111] magnetic field

Spin ice in a magnetic field in the [111] direction displays two magnetization plateaus: one at saturation and an intermediate one with finite entropy. We study the crossovers between the differe ...

Efficient variational diagonalization of fully many-body localized Hamiltonians

We introduce a unitary matrix-product operator (UMPO) based variational method that approximately finds all the eigenstates of fully many-body localized (fMBL) one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed bond dimension of the UMPO ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.

Thermal quenches in spin ice.

We study the diffusion-annihilation process which occurs when spin ice is quenched from a high temperature paramagnetic phase deep into the spin-ice regime, where the excitations--magnetic monopoles--are sparse. We find that due to the Coulomb interaction between the monopoles, a dynamical arrest occurs, in which nonuniversal lattice-scale constraints impede the complete decay of charge fluctuations. This phenomenon is outside the reach of conventional mean-field theory for a two-component Coulomb liquid. We identify the relevant time scales for the dynamical arrest and propose an experiment for detecting monopoles and their dynamics in spin ice based on this nonequilibrium phenomenon.

Equilibration and order in quantum Floquet matter

Over the past decade, remarkable progress has occurred in the physics of closed quantum systems away from equilibrium, culminating in the recent experimental realization of so-called time crystals. This Progress Article surveys these developments.