We study the topology of two-dimensional open systems in terms of the Green's function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems, which indicates the number difference of gapless edge bands arising from the poles and zeros of the Green's function. Meanwhile, we define another topological invariant via the single-particle density matrix, which works for general gapped systems and is equivalent to the former for the case of weak coupling to an environment. We also discuss two applications. For time-reversal-invariant insulators, the Z2 index can be expressed by the invariant of each spin subsystem. As a second application, we consider the proximity effect when an ordinary insulator is coupled to a topological insulator.

Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. The detection of edge states remains an open question in ultracold atom setups. We propose a configuration to implement a topological interface within the experimentally realizable time-reversal invariant Hofstadter model which gives rise to a topological phase boundary at the center of the system, and investigate the influence of two-body interactions on the interface in a fermionic system. The interface can in principle be probed via the spatially resolved compressibility of the system by using a quantum gas microscope. Furthermore, we distinguish the phases through their Hall response and compute a local spin Chern marker which proves the phase separation of two distinct topological many-body phases. The bulk-boundary correspondence for the interacting system is confirmed by computing the edge state spectra at the interface.

We study transport properties and topological phase transition in two-dimensional interacting disordered systems. Within dynamical mean-field theory, we derive the Hall conductance, which is quantized and serves as a topological invariant for insulators, even when the energy gap is closed by localized states. In the spinful Harper-Hofstadter-Hatsugai model, in the trivial insulator regime, we find that the repulsive on-site interaction can assist weak disorder to induce the integer quantum Hall effect, while in the topologically non-trivial regime, it impedes Anderson localization. Generally, the interaction broadens the regime of the topological phase in the disordered system. PACS numbers: xxThe quantum Hall effect (QHE) in the presence of interaction and disorder has been of great interest for a long time.Interactions play an essential role in the fractional QHE [1] and disorder is responsible for the existence of the plateaux in the Hall conductance [2][3][4][5]. For different models, the perfect quantization of conductance can be violated [6][7][8][9][10][11][12][13][14][15][16] or conversely induced [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] by disorder and interaction, respectively. Topological invariants are constructed to classify the resulting transport properties [33][34][35] in systems with bulk energy gaps. General expressions for the invariants of interacting and disordered systems were developed from the perspective of the many-body wave functions (MBW) [36][37][38][39]. Nonetheless, the MBW can be captured numerically only for a rather small size of the interacting system. Equivalent expressions in terms of the single-particle Green's function were developed thereafter, based on the microscopic theory [40][41][42], which are numerically accessible even for infinite systems if translational symmetry (TS) is assumed [43]. arXiv:1805.10491v2 [cond-mat.dis-nn]

We systematically investigate the ground state and elementary excitations of a Bose-Einstein Condensate within a synthetic vector potential, which is induced by the many-body effects and atomlight coupling. For a sufficiently strong inter-atom interaction, we find the condensate undergoes a Stoner-type ferromagnetic transition through the self-consistent coupling with the vector potential. For a weak interaction, the critical velocity of a supercurrent is found anisotropic due to the density fluctuations affecting the gauge field. We further analytically demonstrate the topological ground state with a coreless vortex ring in a 3D harmonic trap and a coreless vortex-antivortex pair in a 2D trap. The circulating persistent current is measurable in the time-of-flight experiment or in the dipolar oscillation through the violation of Kohn theorem.Introduction: Gauge fields play an important role in the modern particle physics, mediating interaction between elementary particles. In condensed matter physics, the gauge fields bring many important phenomena, such as integer/factional quantum Hall effects[1, 2], Laughlin liquids [3] and Hofstadter butterfly spectrum[4], etc. In quantum gas systems, artificial gauge fields can be also generated for neutral atoms in the rotating frame [5,6], or by the atom-light coupling with spatial dependent laser fields [7][8][9] or detuning [10,11]. The latter opens up a new possibility to study many-body physics with gauge potential, and is extended to investigate the spin-orbital coupling problems in similar experiments [12].Besides of the generating by external lasers, it was theoretically proposed that the gauge field can be induced by dipole-dipole interaction between two dipolar or Rydberg atoms [13][14][15]. For many-body systems, some interesting dynamics [16] and excitations[17] within a densitydependent gauge field were investigated in a 1D system. However, considering the finite temperature effects and quantum fluctuations, it is certainly more realistic and demanding to investigate many-body properties in higher dimensional systems, where the effective gauge field may further introduce topological defects and more interesting many-body physics not observable in 1D systems.In this Letter, we systematically investigate the ground state and excitation properties of a (pseudo) spin-1/2 condensate with the interaction-induced gauge field in 2D and 3D systems. We find several new many-body properties: (i) For a sufficiently strong inter-atom interaction, the condensate can have a Stoner-type ferromagnetism through the self-consistent coupling with the synthetic field. (ii) In the weak interaction limit, we calculate the Bogoliubov excitation spectrum of a superfluid current, and show that the critical velocity for dynamical instability becomes anisotropic in space due to density fluctuations within the gauge field. (iii) In a harmonic trap, we show analytic solutions of the condensate ground state, and find a coreless vortex ring around the gauge field

We investigate nonperturbatively the effect of a magnetic dopant impurity on the edge transport of a quantum spin Hall (QSH) insulator. We show that for a strongly coupled magnetic dopant located near the edge of a system, a pair of transmission anti-resonances appear. When the chemical potential is on resonance, interaction effects broaden the anti-resonance width with decreasing temperature, thus suppressing transport for both repulsive and moderately attractive interactions. Consequences for the recently observed QSH insulating phase of the 1-T of WTe2 are briefly discussed.I.