arXiv subjects

Vedant Motamarri

Publications and source records attributed to Vedant Motamarri.

5 recordsLinked to original sources

arXiv2025

Classifying one-dimensional Floquet phases through two-dimensional topological order

Floquet systems display rich phenomena, such as time crystals, with many-body localisation (MBL) protecting the phases from heating. While several types of Floquet phases have been classified, a unified picture of Floquet MBL is still emerging. Static phases have been fruitfully studied via "symmetry topological field theory" (SymTFT), wherein the universal features of $G$-symmetric systems are elucidated by placing them on the boundary of a topological order of one dimension higher. In this work, we provide a SymTFT approach to classifying $G$-symmetric Floquet MBL phases in 1D, for $G$ a finite Abelian group with on-site unitary action. In the SymTFT, these 1D systems correspond to the boundaries of the quantum double associated to $G$, and the classification naturally arises from considering the Lagrangian subgroups and boundary excitations of the quantum double. The classification covers all known Floquet phases while uncovering others previously unexplored, along with bulk features of phases thought to have only boundary signatures. We refer to the latter phases as "dual" time crystals. For static phases, we show how anyons of the quantum double and (string) order parameters provide a natural and simple interpretation of known classification schemes. By extending our framework to the boundaries of twisted quantum doubles, we uncover a new time-crystalline phase with non-onsite symmetry, which cannot be obtained through local, symmetric Hamiltonian drives. We numerically demonstrate evidence for the absolute stability of this phase, and observe that for open boundary conditions it has greater stability to symmetric perturbations. We finally discuss perspectives on using programmable quantum devices to realise and probe the phases we discuss. Our results show that SymTFT provides a powerful approach to unifying phases and features of Floquet systems.

cond-mat.str-el↗

arXiv2024

Refined cyclic renormalization group in Russian Doll model

Focusing on Bethe-ansatz integrable models, robust to both time-reversal symmetry breaking and disorder, we consider the Russian Doll Model (RDM) for finite system sizes and energy levels. Suggested as a time-reversal-symmetry breaking deformation of Richardson's model, the well-known and simplest model of superconductivity, RDM revealed an unusual cyclic renormalization group (RG) over the system size $N$, where the energy levels repeat themselves, shifted by one after a finite period in $\ln N$, supplemented by a hierarchy of superconducting condensates, with the superconducting gaps following the so-called Efimov (exponential) scaling. The equidistant single-particle spectrum of RDM made the above Efimov scaling and cyclic RG to be asymptotically exact in the wideband limit of the diagonal potential. Here, we generalize this observation in various respects. We find that, beyond the wideband limit, when the entire spectrum is considered, the periodicity of the spectrum is not constant, but appears to be energy-dependent. Moreover, we resolve the apparent paradox of shift in the spectrum by a single level after the RG period, despite the disappearance of a finite fraction of energy levels. We also analyze the effects of disorder in the diagonal potential on the above periodicity and show that it survives only for high energies beyond the energy interval of the disorder amplitude. Our analytic analysis is supported with exact diagonalization.

cond-mat.dis-nn↗

arXiv2024

SymTFT out of equilibrium: from time crystals to braided drives and Floquet codes

Symmetry Topological Field Theory (SymTFT) is a framework to capture universal features of quantum many-body systems by viewing them as a boundary of topological order in one higher dimension. This has yielded numerous insights in static low-energy settings. Here we study what SymTFT can reveal about nonequilibrium, focusing on one-dimensional (1D) periodically driven systems and their 2D SymTFTs. In driven settings, boundary conditions (BCs) can be dynamical and can apply both spatially and temporally. We show how this enters SymTFT via topological operators, which we then use to uncover several new results. These include revealing time crystals (TCs) as systems with symmetry-twisted temporal BCs, robust bulk ``dual TCs" in phases thought to be only boundary TCs, generating drive dualities, or identifying 2D Floquet codes as space-time duals to 1D systems with duality-twisted spatial BCs. We also show how, by making duality-twisted BCs dynamical, non-Abelian braiding of duality defects can enter SymTFT, leading to effects such as the exact pumping of symmetry charges between a system and its BCs. We illustrate our ideas for $\mathbb{Z}_2$-symmetric 1D systems, but our construction applies for any finite Abelian symmetry.

cond-mat.str-el↗

arXiv2023

Localization and fractality in disordered Russian Doll model

Motivated by the interplay of Bethe-Ansatz integrability and localization in the Richardson model of superconductivity, we consider a time-reversal symmetry breaking deformation of this model, known as the Russian Doll Model (RDM), and implement diagonal on-site disorder. The localization and ergodicity-breaking properties of the single-particle spectrum are analyzed using a large-energy renormalization group (RG) over the momentum-space spectrum. Based on the above RG, we derive an effective Hamiltonian of the model, discover a fractal phase of non-ergodic delocalized states -- with the fractal dimension different from the paradigmatic Rosenzweig-Porter model -- and explain it in terms of the developed RG equations and the matrix-inversion trick.

cond-mat.dis-nn↗

arXiv2023

Loop ensembles in Stochastic Series Expansion of Two-Dimensional Heisenberg Antiferromagnets

The Stochastic Series Expansion (SSE) method along with resummation over the spin or flavor values maps the partition function of a quantum antiferromagnet to a closely-packed loop gas model in one higher dimension. Earlier work by Nahum et al. has shown that certain closely-packed three-dimensional loop gas models exhibit phases dominated by macroscopic loops, wherein the corresponding joint distribution of loop lengths is Poisson-Dirichlet. On grounds of universality, the same is expected of the ensemble of loops obtained in (2+1)-dimensional quantum antiferromagnets, albeit the loops emerge from a different microscopic origin. We sample the SSE loop ensemble for SU(N) antiferromagnets on a square lattice using Monte Carlo and study how the joint distribution varies with the degree of representation N and inverse temperature $β$. We observe that, for low temperatures and small N($\leq$ 4), the distribution indeed shows characteristics of Poisson-Dirichlet behaviour when antiferromagnetic correlations dominate the system.

cond-mat.stat-mech↗