In some recent papers in which Monte Carlo methods have been used, it has been found that disordered Anderson insulators with Coulomb interactions may become glassy at low temperatures. This was indicated by a non-vanishing value of an order parameter. In the present paper, the transition to a glassy state is investigated analytically for systems with and without Coulomb interactions. For the purposes of the analysis, a system is taken to be in the glassy state if it fails to satisfy the ergodic hypothesis. A transition to non-ergodic behaviour is found for both interacting and non-interacting systems, but the transition for the interacting system is softer and occurs at a higher temperature. The results are subject to certain approximations and assumptions, which are specified.
In some recent papers in which Monte Carlo methods have been used, it has been found that disordered Anderson insulators with Coulomb interactions may become glassy at low temperatures. This was indicated by a non-vanishing value of an order parameter. In the present paper, the transition to a glassy state is investigated analytically for systems with and without Coulomb interactions. For the purposes of the analysis, a system is taken to be in the glassy state if it fails to satisfy the ergodic hypothesis. A transition to non-ergodic behaviour is found for both interacting and non-interacting systems, but the transition for the interacting system is softer and occurs at a higher temperature. The results are subject to certain approximations and assumptions, which are specified.
The random-field spin-1/2 XXZ chains, and the corresponding Anderson insulators of spinless fermions with density-density interaction, have been intensively studied in the context of many-body localization. However, we recently argued [B. Krajewski et al., Phys. Rev. Lett. 129, 260601 (2022)] that the two-body density-density interaction in these models is not generic since only a small fraction of this interaction represents a true local perturbation to the Anderson insulator. Here we study ergodicity of strongly disordered Anderson insulator chains, choosing other forms of the two-body interaction for which the strength of the true perturbation is of the same order of magnitude as the bare two-body interaction. Focusing on the strong-interaction regime, numerical results for the level statistics and the eigenstate thermalization hypothesis are consistent with emergence of ergodicity at arbitrary strong disorder.
This thesis contains four studies of the effects of disorder and randomness on strongly correlated quantum phases of matter. Starting with an itinerant ferromagnet, I first use an order-by-disorder approach to show that adding quenched charged disorder to the model generates new quantum fluctuations in the vicinity of the quantum critical point which lead to the formation of a novel magnetic phase known as a helical glass. Switching to bosons, I then employ a momentum-shell renormalisation group analysis of disordered lattice gases of bosons where I show that disorder breaks ergodicity in a non-trivial way, leading to unexpected glassy freezing effects. This work was carried out in the context of ultracold atomic gases, however the same physics can be realised in dimerised quantum antiferromagnets. By mapping the antiferromagnetic model onto a hard-core lattice gas of bosons, I go on to show the importance of the non-ergodic effects to the thermodynamics of the model and find evidence for an unusual glassy phase known as a Mott glass not previously thought to exist in this model. Finally, I use a mean-field numerical approach to simulate current generation quantum gas microscopes and demonstrate the feasibility of a novel measurement scheme designed to measure the Edwards-Anderson order parameter, a quantity which describes the degree of ergodicity breaking and which has never before been experimentally measured in any strongly correlated quantum system. Together, these works show that the addition of disorder into strongly interacting quantum systems can lead to qualitatively new behaviour, triggering the formation of new phases and new physics, rather than simply leading to small quantitative changes to the physics of the clean system. They provide new insights into the underlying physics of the models and make direct connection with experimental systems which can be used to test the results presented here.
This chapter focuses on studies of the critical behavior of conductivity in two-dimensional electron systems (2DES) with different amounts and types of disorder as well as different ranges of Coulomb interactions, in order to identify possible universality classes of the 2D metal-insulator transition (MIT). It discusses the manifestations of glassiness in both low- and high-disorder samples. The chapter examines the critical region near the 2D MIT in particular on describing conductivity measurements that have demonstrated dynamical scaling, the main signature of the MIT as a quantum phase transition. It also focuses on experiments that probe the nature of the insulating state, as well as charge dynamics across the MIT, in both high- and low-disorder 2DESs. There is substantial evidence that in many materials near the MIT both strong electronic correlations and disorder play an important role, and thus their competition is expected to lead to glassy behavior of electrons, in analogy with other frustrated systems.
Ergodicity is a fundamental property of many physical systems which reflects their ability to reach thermal equilibrium during the course of dynamical evolution. In recent years, it has been understood that exceptions to this fundamental behaviour may be possible: as particles become localized by the external disorder, they can fail to form a thermal environment for themselves. Such ‘many-body-localized’ (MBL) systems are perfect insulators, unlike the more familiar band or Mott insulators. That is, the (electrical) conductivity of an MBL system is precisely zero not only in its ground state, but also at finite energy densities, where in ordinary insulators thermally activated transport would dominate. These, along with many other unique properties, have led to an explosion of recent interest in understanding MBL systems, as well as more general, non-ergodic behaviours of quantum many-body systems. What would such systems do, if they do not approach a thermal state? Are there universal aspects to this behaviour, or will every system behave in a different way? On the more applied side, many-body localization might open a new strategy for fighting decoherence. In all current quantum computing attempts, the main difficulty results from the fact that the thermal environment tends to thermalize a qubit, thereby causing decoherence. This has the unwanted consequence of information scrambling: during thermalization, quantum information encoded in the initial state will spread over the entire system and thereby become inaccessible to local measurements. This may not be the case in MBL systems: as a localized environment fails to thermalize, the system can retain some local information about its initial state for indefinite amounts of time, opening up new possibilities for quantum technologies.
Originally proposed by Anderson in 1958 [1], disorder-induced localization was initially mostly studied as a single-particle phenomenon—dubbed Anderson localization. As a paradigmatic quantum phenomenon, Anderson …
We consider an electron system under conditions of strong Anderson localization, taking into account interelectron long-range Coulomb repulsion. We have established that with the electron density going to zero the Coulomb interaction brings the arrangement of the Anderson localized electrons closer and closer to an ideal (Wigner) crystal lattice, provided the temperature is sufficiently low and the dimension of the system is > 1. The ordering occurs despite the fact that a random spread of the energy levels of the localized one-electron states, exceeding the mean Coulomb energy per electron, renders it impossible the electrons to be self-localized due to their mutual Coulomb repulsion This differs principally the Coulomb ordered Anderson localized electron system (COALES) from Wigner crystal, Wigner glass, and any other ordered electron or hole system that results from the Coulomb self-localization of electrons/holes. The residual disorder inherent to COALES is found to bring about a multi-valley ground-state degeneration akin to that in spin glass. With the electron density increasing, COALES is revealed to turn into Wigner glass or a glassy state of a Fermi-glass type depending on the width of the random spread of the electron levels.
We present a theory for disordered interacting electrons that can describe both the Mott and Anderson transitions in the respective limits of zero disorder and zero interaction. We use it to investigate the T=0 Mott-Anderson transition at a fixed electron density, as the disorder strength is increased. Surprisingly, we find two critical values of disorder Wnfl and Wc. For W>Wnfl, the system enters a ``Griffiths'' phase, displaying metallic non-Fermi liquid behavior. At even stronger disorder, W=Wc>Wnfl the system undergoes a metal-insulator transition, characterized by the linear vanishing of both the typical density of states and the typical quasiparticle weight.