Abstract :

Selective excitation of a diffusive system’s transmission eigenchannels enables manipulation of its internal energy distribution. The fluctuations and correlations of the eigenchannels’ spatial profiles, however, remain unexplored so far. Here we show that the depth profiles of high-transmission eigenchannels exhibit low realization-to-realization fluctuations. Furthermore, our experimental and numerical studies reveal the existence of inter-channel correlations, which are significant for low-transmission eigenchannels. Because high-transmission eigenchannels are robust and independent from other eigenchannels, they can reliably deliver energy deep inside turbid media.

Abstract:

I will present our current understanding of this novel dynamic quantum phase transition as obtained from a strong-randomness real-space renormalization group (RG) approach. This is for the case of isolated one-dimensional quantum many-body systems with quenched randomness and short-range interactions. The RG flow is qualitatively like the famous Kosterlitz-Thouless RG, but is different in some important features, thus making a new universality class of phase transition.

Ref: Morningstar, Huse and Imbrie, Phys. Rev. B 102, 125134 (2020)

Abstract:
In low dimensions, arbitrarily weak disorder induces Anderson localization at large length scales. The ergodic phase of an isolated, low-dimensional dirty fermion system arises due to inelastic carrier-carrier scattering. Quantum conductance corrections are dephased via the thermal noise bath mediated by inelastic collisions. In solid-state systems, dynamically screened Coulomb interactions give rise to an effectively Markovian bath; as shown by Altshuler, Aronov, and Khmelnitsky (AAK), this dephases the lowest order weak localization correction at any nonzero temperature [1]. On the other hand, a system of fermions with pure short-ranged interactions (as could be realized with ultracold atoms) generates a strongly non-Markovian, diffusive bath. The exact AAK solution exploits a transfer-matrix mapping for the Markovian bath, but this is no longer possible in the non-Markovian case. Dephasing weak localization due to the diffusive bath is in fact equivalent to solving a strongly coupled, auxiliary quantum field theory in d < 4 spatial dimensions [2]. I will discuss our attempts to tackle dephasing by a diffusive bath. Using a 4 - epsilon expansion, we show that vertex corrections (disallowed in the Markovian case) suppress the coupling to the bath, opening up the possibility of a nontrivial critical point [2]. We have also studied quasi-1D systems. We show that straight-forward perturbation theory invalidates the self-consistent Born approximation. On the other hand, for a many-channel quantum wire possessing both long-range Coulomb and short-ranged spin-exchange scattering, we find that perturbation theory in the latter is well-behaved when Coulomb scattering is treated exactly via an extension of the AAK technique. Our results indicate that higher-order "rephasing" corrections could play an important role in the pure diffusive bath problem. In solid-state wires, we also provide a new mechanism for the apparent "saturation" of the dephasing time observed in various experiments, due to the enhancement of the triplet coupling at low-temperatures [3].

[1] B. L. Altshuler, A. G. Aronov, and D. E. Khmelnitsky, "Effects of electron-electron collisions with small energy transfers on quantum localisation," J. Phys. C 15, 7367 (1982).
[2] Y. Liao and M. S. Foster, "Dephasing Catastrophe in 4 - epsilon Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase," Phys. Rev. Lett. 120, 236601 (2018).
[3] S. M. Davis and M. S. Foster, "Non-Markovian dephasing of disordered quasi-one-dimensional fermion systems, arXiv:2004.07245.

Abstract:

A longstanding open problem in condensed matter physics is whether or not a strongly disordered interacting insulator can be mapped to a system of effectively non-interacting localized excitations. We investigate this issue on the insulating side of the 3D metal-insulator transition (MIT) in phosphorus doped silicon using the new technique of terahertz two dimensional coherent spectroscopy. Despite the intrinsically disordered nature of these materials, we observe coherent excitations and strong photon echoes that provide us with a powerful method for the study of their decay processes. We extract the first measurements of energy relaxation (T1) and decoherence (T2) times close to the MIT in this classic system. We observe that (i) both relaxation rates are linear in excitation frequency with a slope close to unity, (ii) the energy relaxation timescale T1 counterintuitively increases with increasing temperature and (iii) the coherence relaxation timescale T2 has little temperature dependence between 5 K and 25 K, but counterintuitively increases as the material is doped towards the MIT. We argue that these features imply that (a) the system behaves as a well isolated electronic system on the timescales of interest, and (b) relaxation is controlled by electron-electron interactions. We discuss the potential relaxation channels that may explain the behavior. Our observations constitute a qualitatively new phenomenology, driven by the interplay of strong disorder and strong electron-electron interactions, which we dub the marginal Fermi glass.

Abstract:

The multifractality provides a way of ergodicity breaking in term of chaotization and equipartitioning over degrees of freedom. On the other hand, in quantum information theory it is the entanglement entropy which represents the main measure of ergodicity and thermalization. In this talk I will represent an exact relation between the above measures, showing that the fractal dimension of the non-ergodic wave function puts an upper bound on its entanglement entropy. I will also provide an explicit example demonstrating that the entanglement entropy may reach its ergodic (Page) value when the wave function is still highly non-ergodic and occupies a zero fraction of the total Hilbert space.

Abstract:

We study the many-body multifractality of the Bose-Hubbard Hamiltonian's eigenstates in Fock space, for arbitrary values of the interparticle interaction. For the ground state, the dependence of generalized fractal dimensions (GFD) on interaction strength unambiguously signal the emergence of a Mott insulator, and encodes the critical point of the superfluid to insulator transition [1]. Additionally, we identify the chaotic phase of the Hamiltonian by the energy-resolved correlation between spectral features and structural changes of the associated eigenstates as exposed by the GFD [2]. Within the chaotic phase, the eigenvectors are shown to become ergodic in the thermodynamic limit, in the configuration space Fock basis, in which random matrix theory offers a remarkable description of their typical structure. The convergence of the eigenvectors towards ergodicity, however, is ever more distinct from random matrix theory as the Hilbert space dimension grows.

[1] J. Lindinger, A. Buchleitner, A. Rodríguez, Phys. Rev. Lett. 122, 106603 (2019).

[2] L. Pausch, E. G. Carnio, A. Rodríguez, A. Buchleitner, arXiv:2009.05295 (2020).

Abstract:

Many-body electronic phases can be induced by a magnetic field in dilute fermionic systems. This is the case when all the charge carriers of a Fermi sea are confined in the lowest Landau level, the so-called quantum limit. In this presentation I will discuss the behavior of three dimensional charge carriers of two distinct electronic systems in their quantum limit regime: graphite (a semi-metal) and InAs (a narrow gap semi-conductor). I will show that in both cases, the magnetic field drastically affects their electronic and thermodynamic properties, but in a different way. In graphite, the magnetic field induces a succession a thermodynamic phase transitions accompanied by an extending regime of critical fluctuation at low temperature while in InAs the magnetic field induces a metal-insulator transition (due to localization effects) accompanied by a colossal thermo-electric response. The comparison of both systems points to the existence of distinct edge states and shows the rich variety of electronic properties that can be found in the quantum limit of 3D metals.

Abstract:

Recent experiments in twisted bilayer graphene have set off a flurry of work due to the observation of purportedly correlated phases at the so-called "magic-angle.'" However, the current models in the literature for magic-angle graphene suffer from two flaws: they assume commensurate twist angles and have great difficulty modeling the exact experimental setup where patches of different twist angles appear ("twist disorder"). We introduce and study a family of microscopic models that begins to address these concerns. In these models, the twist angle enters as a free parameter in real space. We can use this to simulate both incommensurate effects and disorder effects. We find that incommensuration leads to an Anderson-like delocalization transition in momentum space. The result is a small metallic phase at the "magic-angle" (that we speculate is unstable to correlated phases). We further study twist-disorder effects and find that while the minibandwidth is renormalized substantially, the Fermi velocity is not significantly altered.

Abstract:

The integer quantum Hall to insulator transition has been mainly studied from the perspective of disordered non-interacting electrons in the lowest Landau level. In this talk, I'll present a dual representation of this critical point using the composite-fermion framework. I'll explain the advantages of this description over the traditional electron version. Employing a mean-field description, I'll present a numerical study of the critical exponents that are in agreement with the Chalker-Coddington network model. Further, I'll show how the fluctuations of the emergent gauge field can lead to the dynamic scaling law and superuniversality of quantum Hall transitions.

Abstract:

This talk reviews and motivates the author's recent proposal of a conformal field theory (CFT) for the scaling limit of the integer quantum Hall (IQH) transition. In particular, the talk will address the following questions: 1. Why does Pruisken's model not qualify as a field theory of the IQH transition? 2. What determines the level of the CFT-IQH current algebra to be n=4? 3. How does the rank of the CFT target space get reduced by a novel form of spontaneous symmetry breaking?