Isolated Quantum Systems: Dynamics and Phase Structure Far From Equilibrium

Statistical mechanics characterizes systems in or near equilibrium using in terms of a handful of "state" variables, e.g. temperature, rather than infinitely many degrees of freedom. Statistical physics describes the expansion of the early universe, aspects of black holes, and most fruitfully, phases of matter and their properties. Quantum considerations have improved this understanding over time and revealed new phenomena, especially in complicated "strongly correlated" systems. Topological phases of matter, e.g., are of both fundamental and practical interest: these phases cannot be distinguished locally, unlike ice and water, which also allows them to store and process quantum information in a "fault-tolerant" manner, recently proposed for application to quantum computation. However, above zero temperature, thermal effects can overwrite this information.Recent experiments on isolated systems have raised fundamental questions and revealed new routes to quantum computing. We now know that entanglement, generated dynamically as a quantum state evolves, "hides" local information about the past, producing familiar equilibrium states, described by a temperature. However, many systems do not thermalize: strong disorder can lead to MBL, which supports numerous phenomena forbidden in equilibrium and can protect quantum information at infinite temperature. In particular, both MBL and thermal systems are robust phases of matter, with a novel, athermal phase transition between them. This thesis begins with an overview of MBL and thermalization, followed by an overview of exactly soluble quantum systems. We then turn to an important result in the field by this author: we introduce the first nontrivial example of an integrable Floquet model and comment on its solution and salient features. We then discuss how integrable models can provide insight into quantum thermalization, e.g. in terms of entanglement growth and demonstrating that conserved charges diffuse. We then investigate thermalization away from the integrable limit, also known as "quantum chaos." We review the standard techniques in this field and, briefly, several important results, before reproducing work by this author establishing definitively the long-conjectured result that the onset of thermalization in the presence of a conserved charge is governed by diffusion of said charge. We then investigate the interplay of conventional and topological order with nonequilibrium phase structure, with applications to quantum computation in mind. We review localization-protected quantum order in several models. We then investigate two models with non-Abelian symmetry, and show that MBL in such models can only realize if the symmetry breaks spontaneously to an Abelian subgroup. Finally, we conclude by examining open quantum systems, where we find several counterintuitive results that show that baths can, in some cases, enhance localization in certain systems, which may have use in realizing quantum computation

The dogged persistence of the British 'old boy': how private school alumni reach the elite

The mythical figure of the public-school ‘Old Boy’ has long had a hold on the British cultural imagination. But, as Aaron Reeves and Sam Friedman explain, alumni of elite schools continue to enjoy very real advantages in reaching the elite

Quantum Brownian motion in a quasiperiodic potential

We consider a quantum particle subject to Ohmic dissipation, moving in a bichromatic quasiperiodic potential. In a periodic potential the particle undergoes a zero-temperature localization-delocalization transition as dissipation strength is decreased. We show that the delocalized phase is absent in the quasiperiodic case, even when the deviation from periodicity is infinitesimal. Using the renormalization group, we determine how the effective localization length depends on the dissipation. We show that {a similar problem can emerge in} the strong-coupling limit of a mobile impurity moving in a periodic lattice and immersed in a one-dimensional quantum gas.Comment: 5+6 pages, 1 figur

From aristocratic to ordinary: shifting modes of elite distinction

How do elites signal their superior social position via the consumption of culture? We address this question by drawing on 120 years of “recreations” data (N = 71,393) contained within Who’s Who, a unique catalogue of the British elite. Our results reveal three historical phases of elite cultural distinction: first, a mode of aristocratic practice forged around the leisure possibilities afforded by landed estates, which waned significantly in the late-nineteenth century; second, a highbrow mode dominated by the fine arts, which increased sharply in the early-twentieth century before gently receding in the most recent birth cohorts; and, third, a contemporary mode characterized by the blending of highbrow pursuits with everyday forms of cultural participation, such as spending time with family, friends, and pets. These shifts reveal changes not only in the contents of elite culture but also in the nature of elite distinction, in particular, (1) how the applicability of emulation and (mis)recognition theories has changed over time, and (2) the emergence of a contemporary mode that publicly emphasizes everyday cultural practice (to accentuate ordinariness, authenticity, and cultural connection) while retaining many tastes that continue to be (mis)recognized as legitimate

Localization-protected order in spin chains with non-Abelian discrete symmetries

We study the non-equilibrium phase structure of the three-state random quantum Potts model in one dimension. This spin chain is characterized by a non-Abelian $D_3$ symmetry recently argued to be incompatible with the existence of a symmetry-preserving many-body localized (MBL) phase. Using exact diagonalization and a finite-size scaling analysis, we find that the model supports two distinct broken-symmetry MBL phases at strong disorder that either break the ${\mathbb{Z}_3}$ clock symmetry or a ${\mathbb{Z}_2}$ chiral symmetry. In a dual formulation, our results indicate the existence of a stable finite-temperature topological phase with MBL-protected parafermionic end zero modes. While we find a thermal symmetry-preserving regime for weak disorder, scaling analysis at strong disorder points to an infinite-randomness critical point between two distinct broken-symmetry MBL phases.Comment: 5 pages, 3 figures main text; 6 pages, 3 figures supplemental material; Version 2 includes a corrected the form of the chiral order parameter, and corresponding data, as well as larger system size numerics, with no change to the phase structur

Particle-hole symmetry, many-body localization, and topological edge modes

We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders.Comment: 9 pages. 7 figure

Is there an old girls’ network? Girls’ schools and recruitment to the British elite

Private schools have long played a crucial role in male elite formation but their importance to women’s trajectories is less clear. In this paper, we explore the relationship between girls’ private schools and elite recruitment in Britain over the past 120 years–drawing on the historical database of Who’s Who, a unique catalogue of the elite. We find that alumni of elite girls schools have been around 20 times more likely than other women to reach elite positions. They are also more likely to follow particular channels of elite recruitment, via the universities of Oxford and Cambridge, private members clubs and elite spouses. Yet such schools have also consistently been less propulsive than their male-only counterparts. We argue this is rooted in the ambivalent aims of girls elite education, where there has been a longstanding tension between promoting academic achievement and upholding traditional processes of gendered social reproduction