Explicit Local Integrals of Motion for the Many-Body Localized State

Recently, it has been suggested that the Many-Body Localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert space preserving renormalization scheme that iteratively finds such integrals of motion exactly. Our method is based on the consecutive action of a similarity transformation using displacement operators. We show, as a proof of principle, localization and the delocalization transition in interacting fermion chains with random onsite potentials. Our scheme of consecutive displacement transformations can be used to study Many Body Localization in any dimension, as well as disorder-free Hamiltonians.Comment: 5 pages, 2 figures, and Supplementary Information. Second version contains new numerical result

Charge-transfer insulation in twisted bilayer graphene

We studied the real space structure of states in twisted bilayer graphene at the `magic angle' $\theta = 1.08^\circ$. The flat bands close to charge neutrality are composed of a mix of `ring' and `center' orbitals around the AA stacking region. An effective model with localized orbitals is constructed, which necessarily includes more than just the four flat bands. Long-range Coulomb interaction causes a charge-transfer at half-filling of the flat bands from the `center' to the `ring' orbitals. Consequently, the Mott phase is a featureless spin-singlet paramagnet. We estimate the effective Heisenberg coupling that favors the singlet coupling to be $J = 3.3$ K, consistent with experimental values. The superconducting state depends on the nature of the dopants: hole-doping yields $p+ip$-wave whereas electron-doping yields $d+id$-wave pairing symmetry.Comment: 8 pages, 6 figures. This second version contains more detailed computations on the Coulomb energy from the unequal charge distributio

Quantum Thermalization and the Expansion of Atomic Clouds

The ultimate consequence of quantum many-body physics is that even the air we breathe is governed by strictly unitary time evolution. The reason that we perceive it nonetheless as a completely classical high temperature gas is due to the incapacity of our measurement machines to keep track of the dense many-body entanglement of the gas molecules. The question thus arises whether there are instances where the quantum time evolution of a macroscopic system is qualitatively different from the equivalent classical system? Here we study this question through the expansion of noninteracting atomic clouds. While in many cases the full quantum dynamics is indeed indistinguishable from classical ballistic motion, we do find a notable exception. The subtle quantum correlations in a Bose gas approaching the condensation temperature appear to affect the expansion of the cloud, as if the system has turned into a diffusive collision-full classical system.Comment: 6 pages, 4 figures, and a 4-page supplementary informatio

Exact Ground State of Lieb-Mattis Hamiltonian as a Superposition of N\'eel states

We show that the exact ground state of the Lieb-Mattis Hamiltonian is an equal-weight superposition of all possible classical N\'{e}el states, and provide an exact formulation of this superposition in the $z$-spin basis for both $S=1/2$ and general $S$ using Schwinger bosons. In general, a superposition of possible rotations on a general initial state is symmetric if and only if the initial state has a nonzero overlap with a singlet state and is otherwise made up of states that vanish due to the symmetrization. Most notably, $|s, m=0 \rangle$ states will vanish if symmetrized, which explains how a superposition of N\'{e}el states projects onto its singlet component.Comment: 7 page

Construction of Many-Body Eigenstates with Displacement Transformations

Many-body eigenstates beyond the gaussian approximation can be constructed in terms of local integrals of motion (IOM), although their actual computation has been until now a daunting task. We present a new practical computation of IOMS based on displacement transformations. It represents a general and systematic way to extend Hartree-Fock and configuration interaction theories to higher order. Our method combines minimization of energy and energy variance of a reference state with exact diagonalization. We show that our implementation is able to perform ground state calculations with high precision for relatively large systems. Since it keeps track of the IMO's forming a reference state, our method is particularly efficient dealing with excited states, both in accuracy and the number of different states that can be constructed

Enhanced superconductivity due to forward scattering in FeSe thin films on SrTiO3 substrates

We study the consequences of an electron-phonon ($e$-$ph$) interaction that is strongly peaked in the forward scattering ($\mathbf{q} = 0$) direction in a two-dimensional superconductor using Migdal-Eliashberg theory. We find that strong forward scattering results in an enhanced $T_c$ that is linearly proportional to the strength of the dimensionless $e$-$ph$ coupling constant $\lambda_m$ in the weak coupling limit. This interaction also produces distinct replica bands in the single-particle spectral function, similar to those observed in recent angle-resolved photoemission experiments on FeSe monolayers on SrTiO$_3$ and BaTiO$_3$ substrates. By comparing our model to photoemission experiments, we infer an $e$-$ph$ coupling strength that can provide a significant portion of the observed high $T_c$ in these systems.Comment: Main text 5 pages, 4 figures; and Supplementary Informatio

Avoiding Stripe Order: Emergence of the Supercooled Electron Liquid

In the absence of disorder, electrons can display glassy behavior through supercooling the liquid state, avoiding the solidification into a charge ordered state. Such supercooled electron liquids are experimentally found in organic $\theta$-$MM'$ compounds. We present theoretical results that qualitatively capture the experimental findings. At intermediate temperatures, the conducting state crosses over into a weakly insulating pseudogap phase. The stripe order phase transition is first order, so that the liquid phase is metastable below $T_s$. In the supercooled liquid phase the resistivity increases further and the density of states at the Fermi level is suppressed, indicating kinetic arrest and the formation of a glassy state. Our results are obtained using classical Extended Dynamical Mean Field Theory.Comment: 4 pages, 4 figures, submitted to the proceedings of "Superstripes 2015", Journal of Superconductivity and Novel Magnetism (2015

Suppressed Density of States in Self-Generated Coulomb Glasses

We investigate the structure of metastable states in self-generated Coulomb glasses. In dramatic contrast to disordered electron glasses, we find that these states lack marginal stability. Such absence of marginal stability is reflected by the suppression of the single-particle density of states into an exponentially soft gap of the form $g(\epsilon) \sim e^{-V / \xi |\epsilon|}$. To analytically explain this behavior, we extend the stability criterion of Efros and Shklovskii to incorporate local charge correlations, in qualitative agreement with our numerical findings. Our work suggests the existence of a new class of self-generated glasses dominated by strong geometric frustration.Comment: v3 is the published version in New Journal of Physic

Influence of long-range interactions on charge ordering phenomena on a square lattice

Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice with fixed particle density, we have identified several interesting phases; such as a generalization of Wigner crystals at low particle densities and stripe phases at densities in between rho = 1/3 and rho = 1/2. These stripes act as domain walls in the checkerboard phase present at half-filling. The phases are characterised at zero temperatures using numerical simulations, and mean field theory is used to construct a finite temperature phase diagram.Comment: 8 pages, 8 figure

Phonon linewidth due to electron-phonon interactions with strong forward scattering in FeSe thin films on oxide substrates

The discovery of an enhanced superconducting transition temperature $T_c$ in monolayers of FeSe grown on several oxide substrates has opened a new route to high-$T_c$ superconductivity through interface engineering. One proposal for the origin of the observed enhancement is an electron-phonon (e-ph) interaction across the interface that peaked at small momentum transfers. In this paper, we examine the implications of such a coupling on the phononic properties of the system. We show that a strong forward scattering leads to a sizable broadening of phonon lineshape, which may result in charge instabilities at long-wavelengths. However, we further find that the inclusion of Coulombic screening significantly reduces the phonon broadening. Our results show that one might not expect anomalously broad phonon linewidths in the FeSe interface systems, despite the fact that the e-ph interaction has a strong peak in the forward scattering (small $q$) direction.Comment: 8 pages, 4 figure