Siddharth Parameswaran

Abstract:

We devise tractable models of unitary quantum many-body dynamics on tree graphs, as a first step toward a deeper understanding of dynamics in non-Euclidean spaces. To this end, we first demonstrate how to construct strictly local quantum circuits that preserve the symmetries of trees, such that their dynamical light cones grow isotropically. For trees with coordination number 𝑧, such circuits can be built from 𝑧-site gates. We then introduce a family of gates for which the dynamics are exactly solvable; these satisfy a set of constraints that we term “tree-unitarity.” Notably, tree-unitarity reduces to the previously established notion of dual-unitarity for 𝑧 =2, when the tree reduces to a line. Among the unexpected features of tree-unitarity is a trade-off between “maximum butterfly velocity” dynamics of out-of-time-order correlators and the existence of nonvanishing correlation functions in multiple directions, a tension absent in one-dimensional dual-unitary models and their Euclidean generalizations. We connect the existence of (a wide class of) solvable dynamics with nonmaximal butterfly velocity directly to a property of the underlying circuit geometry called 𝛿-hyperbolicity, and argue that such dynamics can only arise in non-Euclidean geometries. We give various examples of tree-unitary gates, discuss dynamical correlations, out-of-time-order correlators, and entanglement growth, and show that the kicked Ising model on a tree is a physically motivated example of maximum-velocity tree-unitary dynamics.

Abstract:

SciPost Journals Publication Detail SciPost Phys. 19, 086 (2025) Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems

Abstract:

Graphene moiré systems are ideal environments for investigating complex phase diagrams and gaining fundamental insights into the mechanisms that underlie them, as they permit controlled manipulation of electronic properties. Magic-angle twisted trilayer graphene has emerged as a key platform for exploring moiré superconductivity due to the robustness of its superconducting order and the ability to tune its energy bands with an electric field. Here we report the direct observation of two domes of superconductivity in the phase diagram of magic-angle twisted trilayer graphene. The dependence of the superconductivity of doped holes on the temperature, magnetic field and bias current shows that it is suppressed near a specific filling of the moiré flat band, leading to a double dome in the phase diagram within a finite range of the displacement field. The transport properties are also indicative of a phase transition and the potentially distinct nature of superconductivity in the two domes. Hartree–Fock calculations incorporating mild strain yield an incommensurate Kekulé spiral state whose effective spin polarization peaks in the regime where superconductivity is suppressed in the experiments.

Abstract:

We study fermionic quantum spin liquids (QSLs) on the three-dimensional trillium lattice of corner-sharing triangles. We are motivated by recent experimental and theoretical investigations that have explored various classical and quantum spin liquid states on similar networks of triangular motifs with strong geometric frustration. Using the framework of projective symmetry groups (PSG), we obtain a classification of all symmetric ${\mathsf{Z}}_2$ and $\mathsf{U}\left(1\right)$ QSLs on the trillium lattice. We find two ${\mathsf{Z}}_2$ spin-liquids, and a single $\mathsf{U}\left(1\right)$ spin-liquid that is proximate to one of the ${\mathsf{Z}}_2$ states. The small number of solutions reflects the constraints imposed by the nonsymmorphic symmetries in the space group of the trillium lattice. Using self-consistency conditions of the mean-field equations, we obtain the spinon band-structure and spin structure factors corresponding to these states. All three of our spin liquids are gapless at their saddle points: one of the two ${\mathsf{Z}}_2$ QSLs is nodal, while the $\mathsf{U}\left(1\right)$ case hosts a spinon Fermi surface. One of our ${\mathsf{Z}}_2$ spin liquids hosts a stable gapless nodal star that is protected by projective symmetries against additions of further neighbor terms in the mean-field ansatz. We comment on directions for further work.