PhD Conference, 22-23 November 2021
This is an event to network and exchange ideas amongst PhD students that are currently working with Benjamin Doyon and/or Olalla Castro-Alvaredo. The list of participants and timetable of talks are below.
The in-person talks will take place on the 23rd of November at City, University of London, Room C321, Tait Building, Northampton Square Campus (best way to get in, is to use the main entrance in Northampton Square and then ask at the reception desk)
For people attending or speaking on-line the link is
Join Zoom Meeting
https://city-ac-uk.zoom.us/j/81836798218
Meeting ID: 818 3679 8218
Passcode: 707571
The in-person talks will take place on the 23rd of November at City, University of London, Room C321, Tait Building, Northampton Square Campus (best way to get in, is to use the main entrance in Northampton Square and then ask at the reception desk)
For people attending or speaking on-line the link is
Join Zoom Meeting
https://city-ac-uk.zoom.us/j/81836798218
Meeting ID: 818 3679 8218
Passcode: 707571
Day 1 (all talks online)
Dimitrios Ampelogiannis (King's College London)
[22nd November 11:30pm]
Online
Title: Almost everywhere ergodicity in quantum spin lattice models
Abstract: In quantum spin lattice models a key result is the Lieb-Robinson bound, which shows that the spatial extent of the time evolution of operators is exponentially small outside a light-cone, defined by the Lieb-Robinson velocity. This implies a form of ergodicity outside the light-cone, but what happens within it? It turns out that, under general assumptions, ergodicity can be obtained almost everywhere inside the light-cone and indicates that operators get “thinner” in the long-time limit, along almost every space-time ray. I will provide a brief introduction of the mathematical set-up and the necessary assumptions, then move on to precisely state an ergodicity theorem for quantum lattice models and discuss related results.
Abstract: In quantum spin lattice models a key result is the Lieb-Robinson bound, which shows that the spatial extent of the time evolution of operators is exponentially small outside a light-cone, defined by the Lieb-Robinson velocity. This implies a form of ergodicity outside the light-cone, but what happens within it? It turns out that, under general assumptions, ergodicity can be obtained almost everywhere inside the light-cone and indicates that operators get “thinner” in the long-time limit, along almost every space-time ray. I will provide a brief introduction of the mathematical set-up and the necessary assumptions, then move on to precisely state an ergodicity theorem for quantum lattice models and discuss related results.
Luca Capizzi (SISSA, Italy)
[22nd November 12:20pm]
Online
Title : Symmetry resolved entanglement in QFT: Equipartition of entanglement and beyond
Abstract: Entanglement measures turned out to be fundamental tools for a finer description of the quantum world. During the last decades, several entanglement measures have been investigated in the context of many-body quantum systems (von Neumann entropy, negativity, relative entropies...), whose non-local nature challenged the local description provided by Quantum field theories (QFT). In addition, some recent experiments in the context of disordered systems showed that whenever an internal symmetry is present it is also important to understand the “internal symmetry structure” of the entanglement as well. That was a starting point to consider, in addition to "standard" entanglement measures, "symmetry-resolved" versions of them. I will provide an introductory presentation to the subject, focusing on a mechanism dubbed as "equipartition of entanglement", which occurs in (QFT). Moreover, I will discuss some recent exact results regarding the violation of equipartition in lattice models near the critical point, seen as QFTs in presence of a small but finite ultraviolet cutoff.
Abstract: Entanglement measures turned out to be fundamental tools for a finer description of the quantum world. During the last decades, several entanglement measures have been investigated in the context of many-body quantum systems (von Neumann entropy, negativity, relative entropies...), whose non-local nature challenged the local description provided by Quantum field theories (QFT). In addition, some recent experiments in the context of disordered systems showed that whenever an internal symmetry is present it is also important to understand the “internal symmetry structure” of the entanglement as well. That was a starting point to consider, in addition to "standard" entanglement measures, "symmetry-resolved" versions of them. I will provide an introductory presentation to the subject, focusing on a mechanism dubbed as "equipartition of entanglement", which occurs in (QFT). Moreover, I will discuss some recent exact results regarding the violation of equipartition in lattice models near the critical point, seen as QFTs in presence of a small but finite ultraviolet cutoff.
Friedrich Hübner (King's College London)
[22nd November 3:00pm]
Online
Title: Bound fermionic pairs scattering at a resonantly driven impurity
Abstract: Applying external periodically driven fields is a popular way to introduce otherwise uncommon effects in quantum systems. While the periodic drive is often applied to the system as a whole, in recent years there were also ideas of only driving small regions which can be described by effective impurities with interesting properties. We study the scattering of a bound pair in a Fermi-Hubbard chain at such a driven impurity. In this talk I would like to focus on the intricate case of resonant driving. In contrast to the non-resonant case, which has been studied in great detail for decades, the resonant case is generally much more complicated to treat analytically and thus is mostly studied numerically. In the Fermi-Hubbard model resonant driving can lead to pair breaking, where a pair absorbs energy from the driving and breaks into two single particles. I will explain how one can study this pair breaking process analytically and present the surprising result that it actually vanishes in the limit of large frequency and strong interaction.
Abstract: Applying external periodically driven fields is a popular way to introduce otherwise uncommon effects in quantum systems. While the periodic drive is often applied to the system as a whole, in recent years there were also ideas of only driving small regions which can be described by effective impurities with interesting properties. We study the scattering of a bound pair in a Fermi-Hubbard chain at such a driven impurity. In this talk I would like to focus on the intricate case of resonant driving. In contrast to the non-resonant case, which has been studied in great detail for decades, the resonant case is generally much more complicated to treat analytically and thus is mostly studied numerically. In the Fermi-Hubbard model resonant driving can lead to pair breaking, where a pair absorbs energy from the driving and breaks into two single particles. I will explain how one can study this pair breaking process analytically and present the surprising result that it actually vanishes in the limit of large frequency and strong interaction.
Day 2 (all taks in person at City)
Lucía Santamaría Sanz (U. Valladolid, Spain)
[23rd November 11:30am]
In person at City
Title: Vacuum energy and thermal Casimir effect in the presence of boundaries
Abstract: New expressions for the Casimir energy between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium will be obtained. The plates will be mimicked by the most general lossless and frequency-independent boundary conditions allowed by the principles of quantum field theory. The thermal correction to the quantum vacuum energy, the pressure between plates and the quantum thermal correction to the entropy will be computed as functions of the temperature and the boundary condition. The same method will be applied to study the quantum vacuum energy and the thermal corrections for non interacting scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support.
Abstract: New expressions for the Casimir energy between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium will be obtained. The plates will be mimicked by the most general lossless and frequency-independent boundary conditions allowed by the principles of quantum field theory. The thermal correction to the quantum vacuum energy, the pressure between plates and the quantum thermal correction to the entropy will be computed as functions of the temperature and the boundary condition. The same method will be applied to study the quantum vacuum energy and the thermal corrections for non interacting scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support.
Joseph Durning (King's College London)
[23rd November 12:15pm]
In person at City
Title: (Integrable) Transport beyond the Euler scale in the presence of external fields.
Abstract: The earliest full set of hydrodynamic equations to be written were by Euler, with the eponymous equations describing the ballistic propagation of conserved modes. The Navier-Stokes equations constitute the next order in the hydrodynamic expansion, and include diffusive physics in the presence of an external gravitational field. However, the equations in the presence of external fields coupling to arbitrary hydrodynamic modes were (presumably) hitherto unknown. Here I describe how such equations can be obtained, with the diffusion constants expressed in terms of generalised Onsager matrices. Recent studies in 1-dimension have shown the existence of various types of anomalous transport, particularly in integrable and near-integrable systems, ranging from super- to sub-diffusive. I briefly discuss how our diffusive equation fits into the still-evolving picture in 1-dimension, highlighting in particular the diffusive behaviour of integrable systems, where our formalism can be applied.
Abstract: The earliest full set of hydrodynamic equations to be written were by Euler, with the eponymous equations describing the ballistic propagation of conserved modes. The Navier-Stokes equations constitute the next order in the hydrodynamic expansion, and include diffusive physics in the presence of an external gravitational field. However, the equations in the presence of external fields coupling to arbitrary hydrodynamic modes were (presumably) hitherto unknown. Here I describe how such equations can be obtained, with the diffusion constants expressed in terms of generalised Onsager matrices. Recent studies in 1-dimension have shown the existence of various types of anomalous transport, particularly in integrable and near-integrable systems, ranging from super- to sub-diffusive. I briefly discuss how our diffusive equation fits into the still-evolving picture in 1-dimension, highlighting in particular the diffusive behaviour of integrable systems, where our formalism can be applied.
Michele Mazzoni (City, University of London)
[23rd November 3pm]
In person at City
Title: Generalised hydrodynamics of Zamolodchikov's staircase model: from the massless flows picture to higher spin currents"
Abstract: The staircase model is a generalization of the 1+1d sinh-Gordon model which displays some non-trivial features both at the thermodynamic and at the hydrodynamic level, in spite of a very simple scattering theory. The property to which the theory owes its name is the roaming behaviour of its scaling function, which approaches all the unitary minimal conformal models under the action of the renormalisation group. When investigating the hydrodynamics of the model, we find that this behaviour is common to other observables, namely the GGE averages of higher spin currents, for which we also derive a universal scaling law which generalises the result already obtained by B. Doyon and D. Bernard. Another interesting feature of the model is the presence of a strong non-monotonicity in the particle density and the effective velocities: this is the starting point which allows us to build a connection between this model and the non-diagonal massless flows interpolating between adjacent unitary minimal conformal models. We justify this connection and use it to derive a physical interpretation of the staircase model which holds both at and off-thermal equilibrium.
Abstract: The staircase model is a generalization of the 1+1d sinh-Gordon model which displays some non-trivial features both at the thermodynamic and at the hydrodynamic level, in spite of a very simple scattering theory. The property to which the theory owes its name is the roaming behaviour of its scaling function, which approaches all the unitary minimal conformal models under the action of the renormalisation group. When investigating the hydrodynamics of the model, we find that this behaviour is common to other observables, namely the GGE averages of higher spin currents, for which we also derive a universal scaling law which generalises the result already obtained by B. Doyon and D. Bernard. Another interesting feature of the model is the presence of a strong non-monotonicity in the particle density and the effective velocities: this is the starting point which allows us to build a connection between this model and the non-diagonal massless flows interpolating between adjacent unitary minimal conformal models. We justify this connection and use it to derive a physical interpretation of the staircase model which holds both at and off-thermal equilibrium.
Aleksandra A. Ziolkowska (University of Oxford)
[23rd November 3:45pm]
In person at City
Title: Unstable Excitations in an Integrable Quantum Field Theory
Abstract: Scattering processes in integrable theories are traditionally associated with particle number conservation. This is indeed the case for asymptotic states, yet at intermediate timescales decaying excitations are allowed. The family of homogeneous sine-Gordon (HSG) models provides a rare example of an integrable quantum field theory where both stable and unstable bound states are present in the spectrum.
In my talk, I will present a study of a particular member of this family, the SU(3)_2-HSG model, following a non-equilibrium quench. At high temperatures, physical intuition suggests that unstable particles are constantly formed and destroyed, and thus exist in finite proportions. As such, they may be expected to have a strong effect on the dynamics far from equilibrium and at finite densities. Adopting the generalized hydrodynamic approach, we identified the key signatures of unstable excitations which may serve as hallmarks for the finitely-lived bound states formation. Furthermore, we explored in considerable detail quantitative and qualitative dependence of the instability signatures on the quench parameters.
Abstract: Scattering processes in integrable theories are traditionally associated with particle number conservation. This is indeed the case for asymptotic states, yet at intermediate timescales decaying excitations are allowed. The family of homogeneous sine-Gordon (HSG) models provides a rare example of an integrable quantum field theory where both stable and unstable bound states are present in the spectrum.
In my talk, I will present a study of a particular member of this family, the SU(3)_2-HSG model, following a non-equilibrium quench. At high temperatures, physical intuition suggests that unstable particles are constantly formed and destroyed, and thus exist in finite proportions. As such, they may be expected to have a strong effect on the dynamics far from equilibrium and at finite densities. Adopting the generalized hydrodynamic approach, we identified the key signatures of unstable excitations which may serve as hallmarks for the finitely-lived bound states formation. Furthermore, we explored in considerable detail quantitative and qualitative dependence of the instability signatures on the quench parameters.
Giuseppe (Del Vecchio)^2 (King's College London)
[23rd November 4:30pm]
In person at City
Title: The hydrodynamic theory of dynamical correlation functions in the XX chain
Abstract: In this talk I will talk about how large deviation theory in combination with generalised hydrodynamic gives access to large space-time behaviour of order parameters correlation functions in a wide class of one dimensional models at the so-called Euler scale. We will focus on the simple XX spin chain, although the method generalises easily to XY chains, Sine-Gordon field theory and other interacting theories. The exponential decay of the transverse correlation functions for the spin field had been computed in a famous paper by Its and collaborators in the massive regime. We complete the picture, giving the analytical expression for arbitrary magnetic field and along arbitrary directions in space-time supporting results and arguments via numerical simulations.
Abstract: In this talk I will talk about how large deviation theory in combination with generalised hydrodynamic gives access to large space-time behaviour of order parameters correlation functions in a wide class of one dimensional models at the so-called Euler scale. We will focus on the simple XX spin chain, although the method generalises easily to XY chains, Sine-Gordon field theory and other interacting theories. The exponential decay of the transverse correlation functions for the spin field had been computed in a famous paper by Its and collaborators in the massive regime. We complete the picture, giving the analytical expression for arbitrary magnetic field and along arbitrary directions in space-time supporting results and arguments via numerical simulations.