Periodic Reporting for period 3 - Corr-NEQM (Correlated Non-Equilibrium Quantum Matter: Fundamentals and Applications to Nanoscale Systems)
Reporting period: 2022-11-01 to 2024-04-30
Laws of thermodynamics describe a wide range of phenomena in nature. Recently, it was discovered that certain class of interacting quantum systems can fail to thermalize and remain out of equilibrium for infinitely long, a phenomena known as many-body localization (MBL). The breakdown of thermodynamics opens the avenue to realise macroscopic quantum coherence in highly excited states and provide new ways for processing quantum information away from zero temperature. Under the influence of a periodic drive, an MBL system can also exhibit breaking of discrete time-translational symmetry which leads to the formation of time-crystals. The proposal aims to investigate the various aspects of non-equilibrium quantum matter characterised by many-body localisation and time-crystallinity in the presence of coupling to an environment and forms of interactions relevant to solid state systems. These novel quantum states of matter can provide pathways to transport quantum information while mitigating the effects of noise and may not require being close to absolute zero of temperature as required for many quantum phenomena.
Progress on planned projects:
The properties of many-body localization-delocalization in the thermodynamic limit and identification of the critical point remains a challenging problem. We have made progress in characterising the late, but finite, time dynamics in the thermodynamic limit in spin ladders and Fermi-Hubbard chains. Due to larger effective local Hilbert-space dimension and symmetries, these models exhibit instabilities away from localisation.
MBL is characterised by an extensive set of quasi-local conservation laws. We showed that random measurements, a form of unitarity-breaking perturbation in open quantum systems, introduces an entanglement transition distinct from the MBL transition. Deep in the MBL phase, local measurements destroy the volume-law entanglement in the steady state for an arbitrarily small measurement strength. Our result highlights the sensitivity of the MBL phase to an external environment.
We theoretically modelled the formation of discrete time-crystalline (DTC) behaviour in a solid-state system using a driven-dissipative interacting spin model. We found a phase diagram as a function of interaction strength and dissipation with a robust DTC phase. Quantitative agreement was found between the predictions of the theoretical model and experimental observations. We provided a phase diagram for the interplay between localisation and dissipation for time-crystalline behaviour and emphasised the importance of dissipation in describing experimental results on time crystals.
Work in progress
Localization (Single and Many-body) in the presence of dissipation- We are studying the spectral and dynamical properties of an extended quantum system coupled to a Markovian environment and its effect on localisation of single and many-particle systems. We have made significant progress on this and a publication is imminent in the next few months.
Resonances in the MBL phase- We are analysing the resonance structure of approximate eigenstates provided by tensor networks for large system sizes and properties of l-bits in the MBL phases in the presence of a discrete symmetry. By quantifying the proliferation of resonances in the vicinity of the localization-delocalization transition we will provide a detailed understanding of the stability of the MBL phase. We are in the process of preparing a manuscript on this result.
New developments:
There have been some exciting recent developments on non-equilibrium quantum matter which are closely related to the broader aims of the proposal. Some of these questions can be addressed by leveraging the expertise associated with the objectives of the proposal and is highly relevant for maintaining a competitive advantage in this rapidly evolving field.
Quantum scars and Hilbert space fragmentation- Certain systems can be driven away from thermal behaviour even in the absence of disorder, where certain initial states exhibit revivals and transport can be anomalously slow, for certain non-integrable systems. We have shown the formation of ETH violating eigenstates, called many-body quantum scars (MBS), in short-range interacting spin-1/2 models on frustrated and unfrustrated lattices in one and two dimensions. We also show in a certain class of frustration-free spin-1 chain can result in fragmentation of the Hilbert space into disconnected clusters where the system remains in the cluster if the initial conditions are fully confined to it. The transport at infinite temperature in these fragmented clusters was found to be subdiffusive with an exponent distinct from the well-known models with dipole conservation. This slow transport is akin to the behaviour of disordered systems close to the MBL transition.
Chaos and hydrodynamics in quantum circuits- Quantum circuits have generated a great deal of interest as a fertile ground for investigating universal non-equilibrium dynamics. By simulating time-periodic and fully random circuits we have studied the growth of entanglement and hydrodynamics of conserved quantities. In a class of classically stimulable circuits, known as Clifford circuit, we have shown that the light cone properties (scaling with time) can be tuned by introducing long range gates and the hydrodynamic tails are closely related to the light cones with the exponent varying from diffusive to ballistic. Entanglement propagation in long range disordered systems are pertinent to the stability of MBL in the similar settings.
Measurements induced entanglement transitions- Role of measurements on quantum many-body systems provides another lens to study the effect of an external environment on the dynamics. We have characterised the entanglement of quantum trajectories to study the critical properties of the phase transition between volume-law and area-law entangled steady states in one and two dimensional random Clifford circuits. These results will provide deeper understand of the interplay of disorder, interactions and dissipation.
The properties of many-body localization-delocalization in the thermodynamic limit and identification of the critical point remains a challenging problem. We have made progress in characterising the late, but finite, time dynamics in the thermodynamic limit in spin ladders and Fermi-Hubbard chains. Due to larger effective local Hilbert-space dimension and symmetries, these models exhibit instabilities away from localisation.
MBL is characterised by an extensive set of quasi-local conservation laws. We showed that random measurements, a form of unitarity-breaking perturbation in open quantum systems, introduces an entanglement transition distinct from the MBL transition. Deep in the MBL phase, local measurements destroy the volume-law entanglement in the steady state for an arbitrarily small measurement strength. Our result highlights the sensitivity of the MBL phase to an external environment.
We theoretically modelled the formation of discrete time-crystalline (DTC) behaviour in a solid-state system using a driven-dissipative interacting spin model. We found a phase diagram as a function of interaction strength and dissipation with a robust DTC phase. Quantitative agreement was found between the predictions of the theoretical model and experimental observations. We provided a phase diagram for the interplay between localisation and dissipation for time-crystalline behaviour and emphasised the importance of dissipation in describing experimental results on time crystals.
Work in progress
Localization (Single and Many-body) in the presence of dissipation- We are studying the spectral and dynamical properties of an extended quantum system coupled to a Markovian environment and its effect on localisation of single and many-particle systems. We have made significant progress on this and a publication is imminent in the next few months.
Resonances in the MBL phase- We are analysing the resonance structure of approximate eigenstates provided by tensor networks for large system sizes and properties of l-bits in the MBL phases in the presence of a discrete symmetry. By quantifying the proliferation of resonances in the vicinity of the localization-delocalization transition we will provide a detailed understanding of the stability of the MBL phase. We are in the process of preparing a manuscript on this result.
New developments:
There have been some exciting recent developments on non-equilibrium quantum matter which are closely related to the broader aims of the proposal. Some of these questions can be addressed by leveraging the expertise associated with the objectives of the proposal and is highly relevant for maintaining a competitive advantage in this rapidly evolving field.
Quantum scars and Hilbert space fragmentation- Certain systems can be driven away from thermal behaviour even in the absence of disorder, where certain initial states exhibit revivals and transport can be anomalously slow, for certain non-integrable systems. We have shown the formation of ETH violating eigenstates, called many-body quantum scars (MBS), in short-range interacting spin-1/2 models on frustrated and unfrustrated lattices in one and two dimensions. We also show in a certain class of frustration-free spin-1 chain can result in fragmentation of the Hilbert space into disconnected clusters where the system remains in the cluster if the initial conditions are fully confined to it. The transport at infinite temperature in these fragmented clusters was found to be subdiffusive with an exponent distinct from the well-known models with dipole conservation. This slow transport is akin to the behaviour of disordered systems close to the MBL transition.
Chaos and hydrodynamics in quantum circuits- Quantum circuits have generated a great deal of interest as a fertile ground for investigating universal non-equilibrium dynamics. By simulating time-periodic and fully random circuits we have studied the growth of entanglement and hydrodynamics of conserved quantities. In a class of classically stimulable circuits, known as Clifford circuit, we have shown that the light cone properties (scaling with time) can be tuned by introducing long range gates and the hydrodynamic tails are closely related to the light cones with the exponent varying from diffusive to ballistic. Entanglement propagation in long range disordered systems are pertinent to the stability of MBL in the similar settings.
Measurements induced entanglement transitions- Role of measurements on quantum many-body systems provides another lens to study the effect of an external environment on the dynamics. We have characterised the entanglement of quantum trajectories to study the critical properties of the phase transition between volume-law and area-law entangled steady states in one and two dimensional random Clifford circuits. These results will provide deeper understand of the interplay of disorder, interactions and dissipation.
Our method to evaluate the probability distribution of resonances in many-body localized phases will allow us to probe the stability of MBL in a variety of settings relevant to experiments. The interplay between measurements and localization can introduce new ideas for localization in open quantum systems. Random unitary circuits can provide a new perspectives on ergodicity breaking phase transitions and novel solvable limits which can be also relevant to quantum information processing.