This project advances the theoretical understanding of nonequilibrium quantum matter, focusing on many-body localization (MBL), measurement- and dissipation-induced phenomena, quantum circuits, and ergodicity breaking. Combining analytical approaches, numerical methods, and exactly tractable circuit models, we uncovered new mechanisms governing localization breakdown, entanglement transitions, and nonthermal behavior in interacting quantum systems.
Many-Body Localization and Environmental Instability
MBL is characterized by an extensive set of quasi-local conserved quantities that prevent thermalization. We showed that random measurements, serving as unitarity-breaking perturbations, induce an entanglement transition distinct from the MBL transition. Deep in the MBL phase, arbitrarily weak local measurements destroy volume-law entanglement in spin-conserving systems, demonstrating intrinsic fragility to environmental coupling. Systems without spin conservation exhibit a different instability mechanism under weak measurements.
We also characterized non-Hermitian MBL, identifying a two-step transition governed separately by spectral and eigenstate properties. These results establish the sensitivity of localization to environmental effects.
To address the challenge of identifying the localization–delocalization transition in the thermodynamic limit, we implemented numerical linked cluster expansion (NLCE) methods to study transport in disordered spin ladders and Fermi–Hubbard chains. NLCE outperforms finite-size simulations at intermediate disorder. We showed that although spin transport remains delocalized in strongly disordered Hubbard chains with frozen charge, adding a tilted potential strongly suppresses spin transport and produces nonergodic behavior. Complementary work using Clifford-circuit encodings of renormalization group methods demonstrated that resonance proliferation destabilizes localization near phase boundaries.
Dissipation, Monitoring, and Entanglement Transitions
We studied the interplay of localization and continuous monitoring in disordered noninteracting fermions. Monitoring induces localization breakdown and produces logarithmically entangled steady states of quantum trajectories. The resulting critical phase persists up to finite disorder and is consistent with Berezinskii–Kosterlitz–Thouless universality.
In related work on random Lindbladian dynamics, we proposed a model of spinless fermions coupled to local baths via power-law jump operators. Tuning the exponent of the dissipation yields a volume-law to area-law entanglement transition in the mixed steady state, robust against coherent hopping. We further analyzed a one-dimensional free-fermion model subject to frustrated local measurements which was shown to exhibit superdiffusive behavior leading to fractal scaling of the entanglement entropy. These results clarify how measurement and dissipation reshape entanglement in open systems.
Time Crystals and Driven Systems
We modeled discrete time-crystalline behavior in a driven-dissipative interacting spin system relevant to solid-state experiments. Mapping the phase diagram in interaction–dissipation space, we identified a robust DTC phase with quantitative agreement with experiment, highlighting the crucial role of dissipation.
In periodically driven systems, we demonstrated the emergence of a strong zero mode under boundary driving at specific freezing frequencies, associated with an emergent ℤ2 symmetry. This resolves a longstanding question regarding strong zero modes in nonintegrable systems and clarifies thermalization in locally driven matter.
Topological Order and Operator-Space Fragmentation
We established robustness of key features of ℤ2 × ℤ2 symmetry-protected topological order against broad dissipative channels in Lindblad and trajectory frameworks. More generally, we developed a theory of operator-space fragmentation in open systems governed by frustration-free Hamiltonians and structured dissipation. The interplay of unitary and dissipative generator algebras partitions operator space into dynamically disconnected sectors, constraining information spreading and enabling new routes to control entangled states.
Quantum Scars, Fragmentation, and Circuits
We demonstrated many-body quantum scars, ETH-violating eigenstates, in short-range interacting spin systems in one and two dimensions. We further showed that frustration-free spin-1 chains exhibit Hilbert-space fragmentation into disconnected clusters with subdiffusive transport, providing a disorder-free route to slow dynamics analogous to behavior near the MBL transition.
Using random and Floquet quantum circuits, we studied entanglement growth and hydrodynamics. In Clifford circuits with long-range gates, light-cone scaling can be tuned from diffusive to ballistic. We characterized localization instabilities in two-dimensional Floquet circuits and showed that local non-Clifford perturbations in one dimension induce operator-space fragmentation, offering a new mechanism for ergodicity breaking.
The research was presented at dozens of conferences and seminar by the group members.
