Periodic Reporting for period 4 - ConsQuanDyn (Constrained Quantum Dynamics)
Periodo di rendicontazione: 2025-04-01 al 2025-11-30
Recent conceptional and technical progress makes it possible to experimentally prepare and explore strongly-correlated, non-equilibrium quantum states of matter. This progress creates an exciting and interdisciplinary research field that bridges condensed matter, quantum information and atomic physics. The general intuition is that non-equilibrium quantum states relax at late times to their thermal equilibrium following the laws of hydrodynamics. However, the collective response of interacting quantum matter brought far from their thermal equilibrium can also lead to much more spectacular phenomena, including non-trivial relaxation dynamics via prethermal states, dynamical quantum phases that do not even exist in equilibrium, and dynamical phase transitions between these emergent phases. Understanding emergent dynamical properties of interacting quantum matter is hence of central importance both conceptually as well as for interpreting and devising experiments.
Strong interactions and frustration often lead to dynamically constrained excitations of quantum matter. Examples include spin-ice compounds whose spin moments are aligned to fulfil a local ice rule of two spins pointing in and two spins pointing out, frustrated quantum magnets with dimerized excitations, and fracton phases with excitations that are only mobile in certain directions if at all. Recent experiments with synthetic quantum matter has started to explore systems with constrained excitations. While the equilibrium properties of constrained quantum systems have been intensely studied over the last decades, it remains an open challenge to understand their far-from-equilibrium quantum dynamics and the dynamical phases they realize. The central focus of the project ConsQuanDyn is to develop new concepts and new theoretical methods to study constrained quantum systems far from thermal equilibrium.
The project has three principal objectives each of which would represent a major contribution to the field:
(O1) To identify glassy dynamics and hydrodynamic transport in constrained quantum lattice gas, quantum dimer and fracton models.
(O2) To demonstrate information scrambling and entanglement growth in constrained Hilbert spaces.
(O3) To predict exotic dynamical quantum phases and to study their dynamical criticality both in quenched and in periodically driven constrained systems.
To successfully meet our ambitious objectives, we will develop two complementary theoretical approaches based on exact numerical techniques and on non-equilibrium field theory. This allows us to understand fundamental dynamical properties of constrained quantum systems and to guide future experiments. Constrained quantum systems may realize topological quantum bits and self-correcting quantum memories. Due to the international effort of inventing new quantum technology, that inherently operates out of equilibrium, it is now the right time to foster a deep understanding of the non-equilibrium dynamics in constrained quantum matter, which is the central goal of the project ConsQuanDyn.
Strong interactions and frustration often lead to dynamically constrained excitations of quantum matter. Examples include spin-ice compounds whose spin moments are aligned to fulfil a local ice rule of two spins pointing in and two spins pointing out, frustrated quantum magnets with dimerized excitations, and fracton phases with excitations that are only mobile in certain directions if at all. Recent experiments with synthetic quantum matter has started to explore systems with constrained excitations. While the equilibrium properties of constrained quantum systems have been intensely studied over the last decades, it remains an open challenge to understand their far-from-equilibrium quantum dynamics and the dynamical phases they realize. The central focus of the project ConsQuanDyn is to develop new concepts and new theoretical methods to study constrained quantum systems far from thermal equilibrium.
The project has three principal objectives each of which would represent a major contribution to the field:
(O1) To identify glassy dynamics and hydrodynamic transport in constrained quantum lattice gas, quantum dimer and fracton models.
(O2) To demonstrate information scrambling and entanglement growth in constrained Hilbert spaces.
(O3) To predict exotic dynamical quantum phases and to study their dynamical criticality both in quenched and in periodically driven constrained systems.
To successfully meet our ambitious objectives, we will develop two complementary theoretical approaches based on exact numerical techniques and on non-equilibrium field theory. This allows us to understand fundamental dynamical properties of constrained quantum systems and to guide future experiments. Constrained quantum systems may realize topological quantum bits and self-correcting quantum memories. Due to the international effort of inventing new quantum technology, that inherently operates out of equilibrium, it is now the right time to foster a deep understanding of the non-equilibrium dynamics in constrained quantum matter, which is the central goal of the project ConsQuanDyn.
The research of the project ConsQuanDyn focuses on the quantum dynamics of strongly correlated many-body systems with constraints that arise from geometric frustration and strong interactions. Our work in the past reporting period has focused on our three central objectives and we made important progress on all of them:
(a) Constrained hydrodynamic transport
Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics of a few conserved quantities emerges universally in the evolution of any complex quantum system, as strong interactions entangle and effectively mix local degrees of freedom. In this project, we studied how constraints can modify transport. We investigated fractonic quantum matter in which the total charge and in addition the total dipole moment are conserved. We found that ergodic systems with these constraints can escape the conventional scenario of diffusive transport, and display subdiffusive relaxation instead. This unconventional transport has also been experimentally explored in quantum simulators of ultracold atoms subjected to a tilted optical lattice or arises in the relaxation dynamics of the lowest Landau level in quantum Hall systems.
(b) Information scrambling and operator growth in constrained spaces
We have shown, that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. As an example, we studied operator growth characterized by out-of-time-order correlations (OTOCs) in a dipole-conserving fracton system. We have identified a critical point with sub-ballistically moving OTOC front, that separates a ballistic from a dynamically frozen phase of operator growth. This critical point is tied to an underlying localization transition, and we use its associated scaling properties to derive an effective description of the moving operator front via a biased random walk with long waiting times. We, furthermore, evaluated entanglement properties and the quantum information structure of two-dimensional lattice gauge theories which are highly constrained due to the Gauss law. We focused on how higher-from symmetries can be used to elucidate these phases of matter. We have also developed an information theoretic perspective on the emergence of higher-form symmetries and found that the confining and Higgs phase are separated in 2+1D lattice gauge theories by information theoretic transitions, albeit they are adiabatically connected thermodynamically.
(c) Characterizing exotic phases with constraints
Many-body systems with gauge constraints can lead to unconventional phases of matter with topological order. Examples are fractional quantum Hall states and quantum spin liquids. We have developed a quantum algorithm to realize a quantum spin liquid on a superconducting quantum information processor, have simulated anyon braiding and showed how to measure the topological entanglement entropy of the wave function. We have perturbed the fixed point wave function and explored the phase diagram of a 2+1D lattice gauge theory. There, we explored string dynamics on quantum processors and developed numerical tools to probe the roughening transition in the confining phase. We have also analyzed relaxation and thermalization in periodically driven quantum systems and have found a new fractionalized Floquet prethermal regime. In systems with fractionalized excitations the effective Hamiltonian cannot be obtained by a simple high-frequency expansion, as fractionalized excitations couple in general differently to a drive.
Several of our theoretical predictions have been exploited with quantum processors, quantum simulators, as well as quantum materials and thereby been experimentally explored. We have also published manuscripts and uploaded them onto a preprint server for disseminating our results. In summary, with the project ConsQuanDyn, we could further develop the field and improve our understanding of constraint quantum dynamics in quantum many-body systems.
(a) Constrained hydrodynamic transport
Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics of a few conserved quantities emerges universally in the evolution of any complex quantum system, as strong interactions entangle and effectively mix local degrees of freedom. In this project, we studied how constraints can modify transport. We investigated fractonic quantum matter in which the total charge and in addition the total dipole moment are conserved. We found that ergodic systems with these constraints can escape the conventional scenario of diffusive transport, and display subdiffusive relaxation instead. This unconventional transport has also been experimentally explored in quantum simulators of ultracold atoms subjected to a tilted optical lattice or arises in the relaxation dynamics of the lowest Landau level in quantum Hall systems.
(b) Information scrambling and operator growth in constrained spaces
We have shown, that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. As an example, we studied operator growth characterized by out-of-time-order correlations (OTOCs) in a dipole-conserving fracton system. We have identified a critical point with sub-ballistically moving OTOC front, that separates a ballistic from a dynamically frozen phase of operator growth. This critical point is tied to an underlying localization transition, and we use its associated scaling properties to derive an effective description of the moving operator front via a biased random walk with long waiting times. We, furthermore, evaluated entanglement properties and the quantum information structure of two-dimensional lattice gauge theories which are highly constrained due to the Gauss law. We focused on how higher-from symmetries can be used to elucidate these phases of matter. We have also developed an information theoretic perspective on the emergence of higher-form symmetries and found that the confining and Higgs phase are separated in 2+1D lattice gauge theories by information theoretic transitions, albeit they are adiabatically connected thermodynamically.
(c) Characterizing exotic phases with constraints
Many-body systems with gauge constraints can lead to unconventional phases of matter with topological order. Examples are fractional quantum Hall states and quantum spin liquids. We have developed a quantum algorithm to realize a quantum spin liquid on a superconducting quantum information processor, have simulated anyon braiding and showed how to measure the topological entanglement entropy of the wave function. We have perturbed the fixed point wave function and explored the phase diagram of a 2+1D lattice gauge theory. There, we explored string dynamics on quantum processors and developed numerical tools to probe the roughening transition in the confining phase. We have also analyzed relaxation and thermalization in periodically driven quantum systems and have found a new fractionalized Floquet prethermal regime. In systems with fractionalized excitations the effective Hamiltonian cannot be obtained by a simple high-frequency expansion, as fractionalized excitations couple in general differently to a drive.
Several of our theoretical predictions have been exploited with quantum processors, quantum simulators, as well as quantum materials and thereby been experimentally explored. We have also published manuscripts and uploaded them onto a preprint server for disseminating our results. In summary, with the project ConsQuanDyn, we could further develop the field and improve our understanding of constraint quantum dynamics in quantum many-body systems.
The project ConsQuanDyn has already led to several results which go beyond the state of the art. Our overarching goal is to ultimately identify a classification of constrained quantum dynamics and propose new experiments to uncover their fundamental principles.