We demonstrate that crystal defects can act as a probe of intrinsic non-Hermitian topology. In particular, in point-gapped systems with periodic boundary conditions, a pair of dislocations may induce a non-Hermitian skin effect, where an extensive nu
mber of Hamiltonian eigenstates localize at only one of the two dislocations. An example of such a phase are two-dimensional systems exhibiting weak non-Hermitian topology, which are adiabatically related to a decoupled stack of one-dimensional Hatano-Nelson chains. Moreover, we show that strong two-dimensional point gap topology may also result in a dislocation response, even when there is no skin effect present with open boundary conditions. For both cases, we directly relate their bulk topology to a stable dislocation skin effect. Finally, and in stark contrast to the Hermitian case, we find that gapless non-Hermitian systems hosting bulk exceptional points also give rise to a well-localized dislocation response.
In this paper, we characterize quasicrystalline interacting topological phases of matter i.e., phases protected by some quasicrystalline structure. We show that the elasticity theory of quasicrystals, which accounts for both phonon and phason modes,
admits non-trivial quantized topological terms with far richer structure than their crystalline counterparts. We show that these terms correspond to distinct phases of matter and also uncover intrinsically quasicrystalline phases, which have no crystalline analogues. For quasicrystals with internal $mathrm{U}(1)$ symmetry, we discuss a number of interpretations and physical implications of the topological terms, including constraints on the mobility of dislocations in $d=2$ quasicrystals and a quasicrystalline generalization of the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem. We then extend these ideas much further and address the complete classification of quasicrystalline topological phases, including systems with point-group symmetry as well as non-invertible phases. We hence obtain the Quasicrystalline Equivalence Principle, which generalizes the classification of crystalline topological phases to the quasicrystalline setting.
We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints, focusing primarily on those with conserved dipole and higher moments. In the limit of large local Hilbert space dim
ension, we find that the spectral form factor $K(t)$ of Floquet random circuits can be mapped exactly to a classical Markov circuit, and, at late times, is related to the partition function of a frustration-free Rokhsar-Kivelson (RK) type Hamiltonian. Through this mapping, we show that the inverse of the spectral gap of the RK-Hamiltonian lower bounds the Thouless time $t_{mathrm{Th}}$ of the underlying circuit. For systems with conserved higher moments, we derive a field theory for the corresponding RK-Hamiltonian by proposing a generalized height field representation for the Hilbert space of the effective spin chain. Using the field theory formulation, we obtain the dispersion of the low-lying excitations of the RK-Hamiltonian in the continuum limit, which allows us to extract $t_{mathrm{Th}}$. In particular, we analytically argue that in a system of length $L$ that conserves the $m^{th}$ multipole moment, $t_{mathrm{Th}}$ scales subdiffusively as $L^{2(m+1)}$. We also show that our formalism directly generalizes to higher dimensional circuits, and that in systems that conserve any component of the $m^{th}$ multipole moment, $t_{mathrm{Th}}$ has the same scaling with the linear size of the system. Our work therefore provides a general approach for studying spectral statistics in constrained many-body chaotic systems.
Fracton phases exhibit striking behavior which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter. Here, we explore fracton phases from the perspective of defect TQFTs and
show that topological defect networks---networks of topological defects embedded in stratified 3+1D TQFTs---provide a unified framework for describing various types of gapped fracton phases. In this picture, the sub-dimensional excitations characteristic of fractonic matter are a consequence of mobility restrictions imposed by the defect network. We conjecture that all gapped phases, including fracton phases, admit a topological defect network description and support this claim by explicitly providing such a construction for many well-known fracton models, including the X-Cube and Haahs B code. To highlight the generality of our framework, we also provide a defect network construction of a novel fracton phase hosting non-Abelian fractons. As a byproduct of this construction, we obtain a generalized membrane-net description for fractonic ground states as well as an argument that our conjecture implies no type-II topological fracton phases exist in 2+1D gapped systems. Our work also sheds light on new techniques for constructing higher order gapped boundaries of 3+1D TQFTs.
We study the quantum dynamics of a simple translation invariant, center-of-mass (CoM) preserving model of interacting fermions in one dimension (1D), which arises in multiple experimentally realizable contexts. We show that this model naturally displ
ays the phenomenology associated with fractonic systems, wherein single charges can only move by emitting dipoles. This allows us to demonstrate the rich Krylov fractured structure of this model, whose Hilbert space shatters into exponentially many dynamically disconnected subspaces. Focusing on exponentially large Krylov subspaces, we show that these can be either be integrable or non-integrable, thereby establishing the notion of Krylov-restricted thermalization. We analytically find a tower of integrable Krylov subspaces of this Hamiltonian, all of which map onto spin-1/2 XX models of various system sizes. We also discuss the physics of the non-integrable subspaces, where we show evidence for weak Eigenstate Thermalization Hypothesis (ETH) restricted to each non-integrable Krylov subspace. Further, we show that constraints in some of the thermal Krylov subspaces cause the long-time expectation values of local operators to deviate from behavior typically expected from translation-invariant systems. Finally, we show using a Schrieffer-Wolff transformation that such models naturally appear as effective Hamiltonians in the large electric field limit of the interacting Wannier-Stark problem, and comment on connections of our work with the phenomenon of Bloch many-body localization.
We investigate the fate of topological states on fractal lattices. Focusing on a spinless chiral p-wave paired superconductor, we find that this model supports two qualitatively distinct phases when defined on a Sierpinski gasket. While the trivial p
hase is characterized by a self-similar spectrum with infinitely many gaps and extended eigenstates, the novel topological phase has a gapless spectrum and hosts chiral states propagating along edges of the graph. Besides employing theoretical probes such as the real-space Chern number, inverse participation ratio, and energy-level statistics in the presence of disorder, we develop a simple physical picture capturing the essential features of the model on the gasket. Extending this picture to other fractal lattices and topological states, we show that the p+ip state admits a gapped topological phase on the Sierpinski carpet and that a higher-order topological insulator placed on this lattice hosts gapless modes localized on corners.
We discuss the procedure for gauging on-site $mathbb{Z}_2$ global symmetries of three-dimensional lattice Hamiltonians that permute quasi-particles and provide general arguments demonstrating the non-Abelian character of the resultant gauged theories
. We then apply this general procedure to lattice models of several well known fracton phases: two copies of the X-Cube model, two copies of Haahs cubic code, and the checkerboard model. Where the former two models possess an on-site $mathbb{Z}_2$ layer exchange symmetry, that of the latter is generated by the Hadamard gate. For each of these models, upon gauging, we find non-Abelian subdimensional excitations, including non-Abelian fractons, as well as non-Abelian looplike excitations and Abelian fully mobile pointlike excitations. By showing that the looplike excitations braid non-trivially with the subdimensional excitations, we thus discover a novel gapped quantum order in 3D, which we term a panoptic fracton order. This points to the existence of parent states in 3D from which both topological quantum field theories and fracton states may descend via quasi-particle condensation. The gauged cubic code model represents the first example of a gapped 3D phase supporting (inextricably) non-Abelian fractons that are created at the corners of fractal operators.
The entanglement spectrum (ES) provides a barometer of quantum entanglement and encodes physical information beyond that contained in the entanglement entropy. In this paper, we explore the ES of stabilizer codes, which furnish exactly solvable model
s for a plethora of gapped quantum phases of matter. Studying the ES for stabilizer Hamiltonians in the presence of arbitrary weak local perturbations thus allows us to develop a general framework within which the entanglement features of gapped topological phases can be computed and contrasted. In particular, we study models harboring fracton order, both type-I and type-II, and compare the resulting ES with that of both conventional topological order and of (strong) subsystem symmetry protected topological (SSPT) states. We find that non-local surface stabilizers (NLSS), a set of symmetries of the Hamiltonian which form on the boundary of the entanglement cut, act as purveyors of universal non-local features appearing in the entanglement spectrum. While in conventional topological orders and fracton orders, the NLSS retain a form of topological invariance with respect to the entanglement cut, subsystem symmetric systems---fracton and SSPT phases---additionally show a non-trivial geometric dependence on the entanglement cut, corresponding to the subsystem symmetry. This sheds further light on the interplay between geometric and topological effects in fracton phases of matter and demonstrates that strong SSPT phases harbour a measure of quasi-local entanglement beyond that encountered in conventional SPT phases. We further show that a version of the edge-entanglement correspondence, established earlier for gapped two-dimensional topological phases, also holds for gapped three-dimensional fracton models.
We study a model of two species of one-dimensional linearly dispersing fermions interacting via an s-wave Feshbach resonance at zero temperature. While this model is known to be integrable, it possesses novel features that have not previously been in
vestigated. Here, we present an exact solution based on the coordinate Bethe Ansatz. In the limit of infinite resonance strength, which we term the strongly interacting limit, the two species of fermions behave as free Fermi gases. In the limit of infinitely weak resonance, or the weakly interacting limit, the gases can be in different phases depending on the detuning, the relative velocities of the particles, and the particle densities. When the molecule moves faster or slower than both species of atoms, the atomic velocities get renormalized and the atoms may even become non-chiral. On the other hand, when the molecular velocity is between that of the atoms, the system may behave like a weakly interacting Lieb-Liniger gas.
We compute the orbital angular momentum $L_z$ of an s-wave paired superfluid in the presence of an axisymmetric multiply quantized vortex. For vortices with winding number $|k| > 1$, we find that in the weak-pairing BCS regime $L_z$ is significantly
reduced from its value $hbar N k/2$ in the Bose-Einstein condensation (BEC) regime, where $N$ is the total number of fermions. This deviation results from the presence of unpaired fermions in the BCS ground state, which arise as a consequence of spectral flow along the vortex sub-gap states. We support our results analytically and numerically by solving the Bogoliubov-de-Gennes equations within the weak-pairing BCS regime.
