We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions. Applying a combination of Hartree-Fock theory, slave-rotor techniques, and topological arguments, we show that the topological band insulating phase persists up to quite strong interactions. Then we apply the slave-rotor mean-field theory and find a Mott transition at which the charge degrees of freedom become localized on the lattice sites. The spin degrees of freedom, however, are still described by the original Kane-Mele band structure. Gauge field effects in this region play an important role. When the honeycomb layer is isolated then the spin sector becomes already unstable toward an easy plane Neel order. In contrast, if the honeycomb lattice is surrounded by extra "screening" layers with gapless spinons, then the system will support a fractionalized topological insulator phase with gapless spinons at the edges. For large interactions, we derive an effective spin Hamiltonian.

Breaking time-reversal symmetry is a prerequisite for accessing certain interesting many-body states such as fractional quantum Hall states. For polaritons, charge neutrality prevents magnetic fields from providing a direct symmetry breaking mechanism and similar to the situation in ultracold atomic gases, an effective magnetic field has to be synthesized. We show that in the circuit QED architecture, this can be achieved by inserting simple superconducting circuits into the resonator junctions. In the presence of such coupling elements, constant parallel magnetic and electric fields suffice to break time-reversal symmetry. We support these theoretical predictions with numerical simulations for realistic sample parameters, specify general conditions under which time-reversal is broken, and discuss the application to chiral Fock state transfer, an on-chip circulator, and tunable band structure for the Kagome lattice.

We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of such a Jaynes-Cummings lattice thus resembles the physics of the Bose-Hubbard model. We explore this analogy by elaborating on the mean-field theory of the phase transition and by presenting several useful mappings which pinpoint both similarities and differences of the two models. We show that a field-theory approach can be applied to prove the existence of multicritical curves analogous to the multicritical points of the Bose-Hubbard model, and we provide analytical expressions for the position of these curves.

We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice combining the cellular dynamical mean-field theory and its real space extension with analytical approaches. We provide a thorough analysis of the phase diagram and temperature effects at weak spin-orbit coupling. We systematically discuss the stability of the quantum spin Hall phase toward interactions and lattice anisotropy resulting in the plaquette-honeycomb model. We also show the evolution of the helical edge states characteristic of quantum spin Hall insulators as a function of Hubbard interaction and anisotropy. At very weak spin-orbit coupling and intermediate electron-electron interactions, we substantiate the existence of a quantum spin liquid phase.

Although the unit of charge in nature is a fundamental constant, the charge of individual quasiparticles in some low-dimensional systems may be fractionalized. Quantum one-dimensional (1D) systems, for instance, are theoretically predicted to carry charge in units smaller than the electron charge e. Unlike 2D systems, the charge of these excitations is not quantized and depends directly on the strength of the Coulomb interactions. For example, in a 1D system with momentum conservation, it is predicted that the charge of a unidirectional electron that is injected into the wire decomposes into right-and left-moving charge excitations carrying fractional charges f 0 e and (1 − f 0 )e respectively 1,2 . f 0 approaches unity for non-interacting electrons and is less than one for repulsive interactions. Here, we provide the first experimental evidence for charge fractionalization in one dimension. Unidirectional electrons are injected at the bulk of a wire and the imbalance in the currents detected at two drains on opposite sides of the injection region is used to determine f 0 . Our results elucidate further 3,4 the collective nature of electrons in one dimension.Charge fractionalization in one dimension is already predicted for the spinless Luttinger model 1,2 . The charge fraction f 0 is given bywhere g c is the Luttinger-liquid interaction parameter. For a galilean invariant system, g c = v F /v c , where v F is the bare Fermi velocity and v c is the velocity of charge excitations. Roughly,where U is the Coulomb interaction energy and ε F is the Fermi energy. In spinfull one-dimensional (1D) systems, charge fractionalization occurs in addition to spin-charge separation, which has been recently confirmed by spectroscopy and tunnelling experiments [4][5][6] .Observing interaction effects in 1D systems using transport experiments is a considerable challenge. For example, the d.c. twoterminal conductance with ideal contacts is universal and given by G = G 0 ≡ 2e 2 /h, independent of interactions 7-11 . Shot-noise measurements have been useful in detecting fractional charge in 2D systems [12][13][14] . However, low-frequency shot-noise measurements in an ideal wire would only reveal the physics of the Fermi-liquid contacts, remaining insensitive to fractionalization 15 . Although both noise and conductance should reveal interaction effects at frequencies exceeding v F /g c L ∼ 10 10 Hz, where the excitation wavelength is shorter than the wire segment [16][17][18] , these frequencies are difficult to explore experimentally at low temperatures.Initial experimental indication of electron fractionalization in one dimension is provided by angle-resolved photo-emission spectroscopy measurements on stripe-ordered cuprate materials 5 . Recent theoretical studies have proposed transport experiments aimed at detecting the same physics in quantum wires. Generally, these involve the realization of multi-terminal geometries, including: (1) local injection of electrons into a wire, where high-frequency noise correlations are expecte...

No abstract

We present an exact expression for the entanglement entropy generated at a quantum point contact between non-interacting electronic leads in terms of the full counting statistics of charge fluctuations, which we illustrate with examples from both equilibrium and non-equilibrium transport. The formula is also applicable to groundstate entanglement entropy in systems described by non-interacting fermions in any dimension, which in one dimension includes the critical spin-1/2 XX and Ising models where conformal field theory predictions for the entanglement entropy are reproduced from the full counting statistics. These results may play an important role in experimental measurements of entanglement entropy in mesoscopic structures and cold atoms in optical lattices. Introduction.-Entanglement entropy is playing an increasingly important role in describing quantum correlations in many-body systems 1 . For a bipartite system, Fig. 1a, the entanglement entropy of subsystem A is defined as S A = −Tr A {ρ A logρ A }, where the reduced density matrixρ A = Tr B {ρ} is obtained from the full density matrixρ by tracing out the degrees of freedom in the remainder B. For a pure stateρ = |Ψ Ψ|, S A = S B ≡ S. Entanglement entropy is currently being studied theoretically in a wide range of systems including quantum critical systems in one 2-4 and higher