Theory of Condensed MatterCarries out world leading research, broadly categorised under: collective quantum phenomena, first principles quantum mechanical methods, and soft matterhttps://www.repository.cam.ac.uk/handle/1810/198356https://www.repository.cam.ac.uk/retrieve/7a2a2e2f-4e20-40d9-95f0-b19ab568b774/condensed.jpg2024-06-17T21:07:54Z2024-06-17T21:07:54Z181Entanglement negativity and sudden death in the toric code at finite
temperatureHart, OliverCastelnovo, Claudiohttps://www.repository.cam.ac.uk/handle/1810/2784622024-01-05T21:00:01Z2018-04-16T00:00:00Zdc.title: Entanglement negativity and sudden death in the toric code at finite
temperature
dc.contributor.author: Hart, Oliver; Castelnovo, Claudio
dc.description.abstract: We study the fate of quantum correlations at finite temperature in the two
dimensional toric code using the logarithmic entanglement negativity. We are
able to obtain exact results that give us insight into how thermal excitations
affect quantum entanglement. The toric code has two types of elementary
excitations (defects) costing different energies. We show that an
$\mathcal{O}(1)$ density of the lower energy defect is required to degrade the
zero-temperature entanglement between two subsystems in contact with one
another. However, one type of excitation alone is not sufficient to kill all
quantum correlations, and an $\mathcal{O}(1)$ density of the higher energy
defect is required to cause the so-called sudden death of the negativity.
Interestingly, if the energy cost of one of the excitations is taken to
infinity, quantum correlations survive up to arbitrarily high temperatures, a
feature that is likely shared with other quantum spin liquids and frustrated
systems in general, when projected down to their low energy states. We
demonstrate this behaviour both for small subsystems, where we can prove that
the negativity is a necessary and sufficient condition for separability, as
well as for extended subsystems, where it is only a sufficient condition. We
further observe that the negativity per boundary degree of freedom at a given
temperature increases (parametrically) with the size of the boundary, and that
quantum correlations between subsystems with extended boundaries are more
robust to thermal fluctuations.
2018-04-16T00:00:00ZDynamic scaling of topological ordering in classical systemsXu, NCastelnovo, CMelko, RGChamon, CSandvik, AWhttps://www.repository.cam.ac.uk/handle/1810/2778852024-01-07T06:40:27Z2018-01-29T00:00:00Zdc.title: Dynamic scaling of topological ordering in classical systems
dc.contributor.author: Xu, N; Castelnovo, C; Melko, RG; Chamon, C; Sandvik, AW
dc.description.abstract: We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in two and three dimensions. We first consider the three-dimensional Z2 (Ising) lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a nonlocal order parameter (defined using Wilson loops) and a dynamic exponent z=2.70±0.03, the latter in good agreement with previous results for the equilibrium dynamics (autocorrelations). We then study systems where (topological) order forms only at zero temperature - the Ising chain, the two-dimensional Z2 gauge model, and a three-dimensional star model (another variant of the Z2 gauge model). In these systems the correlation length diverges exponentially, in a way that is nonsmooth as a finite-size system approaches the zero temperature state. We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface.
2018-01-29T00:00:00ZSemiclassical dynamics, Berry curvature, and spiral holonomy in optical quasicrystalsSpurrier, SCooper, NRhttps://www.repository.cam.ac.uk/handle/1810/2766072023-12-21T02:17:58Z2018-01-01T00:00:00Zdc.title: Semiclassical dynamics, Berry curvature, and spiral holonomy in optical quasicrystals
dc.contributor.author: Spurrier, S; Cooper, NR
dc.description.abstract: We describe the theory of the dynamics of atoms in two-dimensional
quasicrystalline optical lattices. We focus on a regime of shallow lattice
depths under which the applied force can cause Landau-Zener tunneling past a
dense hierarchy of gaps in the quasiperiodic energy spectrum. We derive
conditions on the external force that allow for a "semiadiabatic" regime in
which semiclassical equations of motion can apply, leading to Bloch
oscillations between the edges of a pseudo-Brillouin-zone. We verify this
semiclassical theory by comparing to the results of an exact numerical
solution. Interesting features appear in the semiclassical dynamics for the
quasicrystal for a particle driven in a cyclic trajectory around the corner of
the pseudo-Brillouin-zone: The particle fails to return to its initial state,
providing a realization of a "spiral holonomy" in the dynamics. We show that
there can appear anomalous velocity contibutions, associated with nonzero Berry
curvature. We relate these to the Berry phase associated with the spiral
holonomy, and show how the Berry curvature can be accessed from the
semiclassical dynamics. Finally, by identifying the pseudo-Brillouin-zone as a
higher genus surface, we show that the Chern number classification for periodic
systems can be extended to a quasicrystal, thereby determining a topological
index for the system.
2018-01-01T00:00:00ZMaterials data validation and imputation with an artificial neural networkVerpoort, PCMacDonald, PConduit, GJhttps://www.repository.cam.ac.uk/handle/1810/2758132023-12-21T01:39:45Z2018-01-01T00:00:00Zdc.title: Materials data validation and imputation with an artificial neural network
dc.contributor.author: Verpoort, PC; MacDonald, P; Conduit, GJ
dc.description.abstract: We apply an artificial neural network to model and verify material
properties. The neural network algorithm has a unique capability to handle
incomplete data sets in both training and predicting, so it can regard
properties as inputs allowing it to exploit both composition-property and
property-property correlations to enhance the quality of predictions, and can
also handle a graphical data as a single entity. The framework is tested with
different validation schemes, and then applied to materials case studies of
alloys and polymers. The algorithm found twenty errors in a commercial
materials database that were confirmed against primary data sources.
2018-01-01T00:00:00ZFerromagnetic-nematic order and strongly correlated phases of fermions in optical flux latticesDavenport, Simon CCooper, Nigel Rhttps://www.repository.cam.ac.uk/handle/1810/2744262023-12-20T22:14:11Z2015-01-01T00:00:00Zdc.title: Ferromagnetic-nematic order and strongly correlated phases of fermions in optical flux lattices
dc.contributor.author: Davenport, Simon C; Cooper, Nigel R
dc.description.abstract: We study a model of a 2D ultracold atomic gas subject to an "optical flux
lattice": a laser configuration where Raman-dressed atoms experience a strong
artificial magnetic field. This leads to a bandstructure of narrow energy bands
with non-zero Chern numbers. We consider the case of two-level (spin-$1/2$)
fermionic atoms in this lattice, interacting via a repulsive $s$-wave contact
interaction. Atoms restricted to the lowest band are described by an effective
model of spinless fermions with interactions that couple states in a
momentum-dependent manner across the Brillouin zone; a consequence of the Raman
dressing of the two spin states. We present the results of detailed exact
diagonalization studies of the many-body states for a range of filling factors,
$\nu$. First, we present evidence for the existence of a phase with coupled
ferromagnetic--nematic ordering, which was previously suggested by a mean-field
analysis. Second, we present evidence indicating the presence of a
Laughlin-like fractional quantum Hall state occurring at filling factor $\nu =
1/3$. Finally, we observe a charge density wave state at $\nu=1/2$, which we
are able to cleanly distinguish from the Laughlin-like state by its
translational symmetry breaking and relatively small participation ratio.
2015-01-01T00:00:00ZBosonic integer quantum Hall effect in optical flux lattices.Sterdyniak, ACooper, Nigel RRegnault, Nhttps://www.repository.cam.ac.uk/handle/1810/2744242024-01-05T17:07:26Z2015-09-11T00:00:00Zdc.title: Bosonic integer quantum Hall effect in optical flux lattices.
dc.contributor.author: Sterdyniak, A; Cooper, Nigel R; Regnault, N
dc.description.abstract: In two dimensions strongly interacting bosons in a magnetic field can realize a bosonic integer quantum Hall state, the simplest two-dimensional example of a symmetry-protected topological phase. We propose a realistic implementation of this phase using an optical flux lattice. Through exact diagonalization calculations, we show that the system exhibits a clear bulk gap and the topological signature of the bosonic integer quantum Hall state. In particular, the calculation of the many-body Chern number leads to a quantized Hall conductance in agreement with the analytical predictions. We also study the stability of the phase with respect to some of the experimentally relevant parameters.
2015-09-11T00:00:00ZSynthetic Spin-Orbit Coupling in an Optical Lattice Clock.Wall, Michael LKoller, Andrew PLi, ShumingZhang, XiboCooper, Nigel RYe, JunRey, Ana Mariahttps://www.repository.cam.ac.uk/handle/1810/2744222024-01-05T17:04:58Z2016-01-22T00:00:00Zdc.title: Synthetic Spin-Orbit Coupling in an Optical Lattice Clock.
dc.contributor.author: Wall, Michael L; Koller, Andrew P; Li, Shuming; Zhang, Xibo; Cooper, Nigel R; Ye, Jun; Rey, Ana Maria
dc.description.abstract: We propose the use of optical lattice clocks operated with fermionic alkaline-earth atoms to study spin-orbit coupling (SOC) in interacting many-body systems. The SOC emerges naturally during the clock interrogation, when atoms are allowed to tunnel and accumulate a phase set by the ratio of the "magic" lattice wavelength to the clock transition wavelength. We demonstrate how standard protocols such as Rabi and Ramsey spectroscopy that take advantage of the sub-Hertz resolution of state-of-the-art clock lasers can perform momentum-resolved band tomography and determine SOC-induced s-wave collisions in nuclear-spin-polarized fermions. With the use of a second counterpropagating clock beam, we propose a method for engineering controlled atomic transport and study how it is modified by p- and s-wave interactions. The proposed spectroscopic probes provide clean and well-resolved signatures at current clock operating temperatures.
2016-01-22T00:00:00ZDynamic Optical Lattices of Subwavelength Spacing for Ultracold Atoms.Nascimbene, SylvainGoldman, NathanCooper, Nigel RDalibard, Jeanhttps://www.repository.cam.ac.uk/handle/1810/2743952024-01-05T17:07:28Z2015-10-02T00:00:00Zdc.title: Dynamic Optical Lattices of Subwavelength Spacing for Ultracold Atoms.
dc.contributor.author: Nascimbene, Sylvain; Goldman, Nathan; Cooper, Nigel R; Dalibard, Jean
dc.description.abstract: We propose a scheme for realizing lattice potentials of subwavelength spacing for ultracold atoms. It is based on spin-dependent optical lattices with a time-periodic modulation. We show that the atomic motion is well described by the combined action of an effective, time-independent lattice of small spacing, together with a micromotion associated with the time modulation. A numerical simulation shows that an atomic gas can be adiabatically loaded into the effective lattice ground state, for time scales comparable to the ones required for adiabatic loading of standard optical lattices. We generalize our scheme to a two-dimensional geometry, leading to Bloch bands with nonzero Chern numbers. The realization of lattices of subwavelength spacing allows for the enhancement of energy scales, which could facilitate the achievement of strongly correlated (topological) states.
2015-10-02T00:00:00ZAnomalous diffusion in a dynamical optical latticeZheng, WCooper, NRhttps://www.repository.cam.ac.uk/handle/1810/2743902023-12-21T06:32:25Z2018-01-01T00:00:00Zdc.title: Anomalous diffusion in a dynamical optical lattice
dc.contributor.author: Zheng, W; Cooper, NR
dc.description.abstract: Motivated by experimental progress in strongly coupled atom-photon systems in
optical cavities, we study theoretically the quantum dynamics of atoms coupled
to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen
to have a period that is incommensurate with that of an underlying static
lattice, leading to a dynamical version of the Aubry-Andr\'e model which can
cause localization of single-particle wavefunctions. We show that atomic
wavepackets in this dynamical lattice generically spread via anomalous
diffusion, which can be tuned between super-diffusive and sub-diffusive
regimes. This anomalous diffusion arises from an interplay between quantum
localization and quantum fluctuations of the cavity field.
2018-01-01T00:00:00ZUniversality of clone dynamics during tissue development.Rulands, SteffenLescroart, FabienneChabab, SamiraHindley, Christopher JPrior, NicoleSznurkowska, Magdalena KHuch, MeritxellPhilpott, AnnaBlanpain, CedricSimons, Benjamin Dhttps://www.repository.cam.ac.uk/handle/1810/2743282024-01-04T23:11:19Z2018-05-01T00:00:00Zdc.title: Universality of clone dynamics during tissue development.
dc.contributor.author: Rulands, Steffen; Lescroart, Fabienne; Chabab, Samira; Hindley, Christopher J; Prior, Nicole; Sznurkowska, Magdalena K; Huch, Meritxell; Philpott, Anna; Blanpain, Cedric; Simons, Benjamin D
dc.description.abstract: The emergence of complex organs is driven by the coordinated proliferation, migration and differentiation of precursor cells. The fate behaviour of these cells is reflected in the time evolution their progeny, termed clones, which serve as a key experimental observable. In adult tissues, where cell dynamics is constrained by the condition of homeostasis, clonal tracing studies based on transgenic animal models have advanced our understanding of cell fate behaviour and its dysregulation in disease (1, 2). But what can be learned from clonal dynamics in development, where the spatial cohesiveness of clones is impaired by tissue deformations during tissue growth? Drawing on the results of clonal tracing studies, we show that, despite the complexity of organ development, clonal dynamics may converge to a critical state characterized by universal scaling behaviour of clone sizes. By mapping clonal dynamics onto a generalization of the classical theory of aerosols, we elucidate the origin and range of scaling behaviours and show how the identification of universal scaling dependences may allow lineage-specific information to be distilled from experiments. Our study shows the emergence of core concepts of statistical physics in an unexpected context, identifying cellular systems as a laboratory to study non-equilibrium statistical physics.
2018-05-01T00:00:00Z