The edge states of the recently proposed quantum spin Hall systems constitute a new symmetry class of one-dimensional liquids dubbed the "helical liquid," where the spin orientation is determined by the direction of electron motion. We prove a no-go theorem which states that a helical liquid with an odd number of components cannot be constructed in a purely 1D lattice system. In a helical liquid with an odd number of components, a uniform gap in the ground state can appear when the time-reversal symmetry is spontaneously broken by interactions. On the other hand, a correlated two-particle backscattering term by an impurity can become relevant while keeping the time-reversal invariance.

The spin 3/2 fermion models with contact interactions have a generic SO(5) symmetry without any fine-tuning of parameters. Its physical consequences are discussed in both the continuum and lattice models. A Monte-Carlo algorithm free of the sign problem at any doping and lattice topology is designed when the singlet and quintet interactions satisfy U0 ≤ U2 ≤ − 3 5 U0 (U0 ≤ 0), thus making it possible to study different competing orders with high numerical accuracy. This model can be accurately realized in ultra-cold atomic systems.PACS numbers: 05.30.Fk, 03.75.Nt, 71.10.Fd, 02.70.Ss With the rapid progress in ultra-cold atomic systems, many alkali fermions have been cooled below Fermi temperatures [1,2,3]. All of them except 6 Li have spins higher than 1/2 in the lowest hyper-fine multiplets. The spin degrees of freedom become free in the optical traps, which has attracted interest in their effects on Cooper pair structures and collective modes [4,5]. The proposal of the optical lattice [6] has led to a tremendous progress in studying the strongly correlated bosonic lattice systems [7,8,9,10,11]. Recently, fermionic lattice systems are also exciting. For example, the degenerate 40 K gas has been prepared in a one-dimensional optical lattice [12].Comprehensive analysis of symmetries is helpful in understanding the physics in strongly correlated systems. For example, the SO(5) theory [13] of high T c cuprates unifies the d-wave superconductivity (SC) and antiferromagnetism (AF) orders, leading to many experimental consequences. The sharp neutron scattering mode can be interpreted as the pseudo-Goldstone mode [13]. The prediction of the antiferromagnetic vortex core [14] has also been verified in recent experiments [15].In this article, we focus on the symmetry properties and corresponding consequences in the spin 3/2 system with contact interactions, including both the continuum model with s-wave scattering and the generalized lattice Hubbard model with on-site interactions. For neutral atoms, these interactions are generally described by two parameters in the total spin S T = 0, 2 channels as g 0,2 = 4πh 2 a 0,2 /M in the continuum model with a 0,2 the corresponding s-wave scattering lengths and M the atom mass; or U 0,2 in the lattice model. Interactions in the odd total spin (S T = 1, 3) channels are forbidden by Pauli's exclusion principle. Remarkably, in addition to the explicit spin SU(2) symmetry, an enlarged SO(5) symmetry is present without any fine tuning of parameters. In the continuum model, this symmetry has direct consequences on the collective modes and pairing structures. In the lattice model, exact phase boundaries of various competing phases can be determined directly from symmetries. Because of the time-reversal symmetry of the Kramers doublets, a Monte-Carlo algorithm free of the notorious sign problem is designed when U 0 ≤ U 2 ≤ −3/5 U 0 (U 0 ≤ 0) at any filling level and lattice topology.We start with the standard form of the spin 3/2 Hamiltonian of the continuum model [4,5] with d the sp...

Optical traps and lattices provide a new opportunity to study strongly correlated high spin systems with cold atoms. In this article, we review the recent progress on the hidden symmetry properties in the simplest high spin fermionic systems with hyperfine spin F = 3/2, which may be realized with atoms of 132 Cs, 9 Be, 135 Ba, 137 Ba, and 201 Hg. A generic SO(5) or isomorphically, Sp(4)) symmetry is proved in such systems with the s-wave scattering interactions in optical traps, or with the on-site Hubbard interactions in optical lattices. Various important features from this high symmetry are studied in the Fermi liquid theory, the mean field phase diagram, and the sign problem in quantum Monte-Carlo simulations. In the s-wave quintet Cooper pairing phase, the half-quantum vortex exhibits the global analogue of the Alice string and non-Abelian Cheshire charge properties in gauge theories. The existence of the quartetting phase, a four-fermion counterpart of the Cooper pairing phase, and its competition with other orders are studied in one dimensional spin-3/2 systems. We also show that counterintuitively quantum fluctuations in spin-3/2 magnetic systems are even stronger than those in spin-1/2 systems.

We consider the problem of two-coupled Luttinger liquids both at half filling and at low doping levels, to investigate the problem of competing orders in quasi-one-dimensional strongly correlated systems. We use bosonization and renormalization group equations to investigate the phase diagrams, to determine the allowed phases, and to establish approximate boundaries among them. Because of the chiral translation and reflection symmetries in the charge mode away from half filling, orders of charge-density wave ͑CDW͒ and spin Peierls ͑SP͒, diagonal current ͑DC͒, and d-density wave ͑DDW͒ form two doublets and thus can be at most quasilong-range ordered. At half filling, Umklapp terms break this symmetry down to a discrete group and thus Ising-type ordered phases appear as a result of spontaneous breaking of the residual symmetries. Quantum disordered Haldane phases are also found, with finite amplitudes of pairing orders and triplet counterparts of CDW, SP, DC, and DDW. Relations with recent numerical results and implications to similar problems in two dimensions are discussed.

Quantum Monte Carlo ͑QMC͒ simulations involving fermions have a notorious sign problem. Some wellknown exceptions to the auxiliary field QMC algorithm rely on the factorizibility of the fermion determinant. Recently, a fermionic QMC algorithm ͓C. Wu, J. Hu, and S. Zhang, Phys. Rev. Lett. 91, 186402 ͑2003͔͒ has been found in which the fermion determinant may not necessarily be factorizable, but can instead be expressed as a product of complex conjugate pairs of eigenvalues, thus eliminating the sign problem for a much wider class of models. In this paper, we present the general conditions for the applicability of this algorithm and point out that it is deeply related to the time-reversal symmetry of the fermion matrix. We apply this method to various models of strongly correlated systems at all doping levels and lattice geometries, and show that many phases can be simulated without the sign problem.

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice. The spin Hall effect has recently attracted strong interest in condensed matter physics because of its connection to quantum Hall physics [1,2] and its potential applications in spintronics [3,4,5,6,7,8,9]. In analogy to the conventional Hall effect related to charge currents, the spin Hall effect refers to the generation of a spin current transverse to an applied electric field. It has been proposed to occur in certain solid-state systems with some primitive experimental demonstration [3]. An essential requirement for observation of the spin Hall effect is generation of an effective spin-dependent gauge potential either in momentum space [5,6,7] or in real space [8]. In both cases, spin-orbit coupling in semiconductors or graphene are employed to provide such mechanisms.It has been widely acknowledged that ultracold atomic gases provide an ideal playground to experimentally investigate some fundamental phenomena originally connected with condensed matter systems [10]. The remarkable controllability in these systems allows a clean study of many complicated physics in a controllable fashion. The generation of an effective gauge potential in atomic systems has raised significant interest, from the earlier implementation of rotating traps [11] to the more recent work on light induced gauge fields [12,13,14,15,16,17,18]. Although most previous work focuses on the study of scalar gauge fields, it is natural to ask whether it is possible to study spin Hall effect in an atomic system.In this paper, we propose an experimental scheme for observation of the spin Hall effects in a cold atomic gas. We show that for atoms with a simple Λ-type three-level configuration moving in a spatially varying laser field, a spin-dependent gauge potential in the real space naturally arises in connection with the Berry phase associated with the atomic motion. Under an applied effective "electric" field, which can be generated from gravity for instance, the atoms will follow a spin-dependent trajectory, which leads to a net spin current in the direction perpendicular to the "electric" and the gauge field while the mass current is zero. Furthermore, we show it is easy to generate different forms of the gauge field in this system, with a strong periodic gauge field as an example. The diverse configurations of the gauge field, in combination with the tunable interaction and the controllable potentials for the atomic gas, may allow us to study various kinds of interesting Hall physics in this system. With this gauge field, we also discuss the associated quantum spin Hall effect for fer...

Spin-orbit coupling plays an important role in determining the properties of solids, and is crucial for spintronics device applications. Conventional spin-orbit coupling arises microscopically from relativistic effects described by the Dirac equation, and is described as a single particle band effect. In this work, we propose a new mechanism in which spin-orbit coupling can be generated dynamically in strongly correlated, non-relativistic systems as the result of fermi surface instabilities in higher angular momentum channels. Various spin-orbit couplings can emerge in these new phases, and their magnitudes can be continuously tuned by temperature or other quantum parameters.PACS numbers: 71.10. Ay, 71.10. Ca, 71.10. Hf Most microscopic interactions in condensed matter physics can be accurately described by non-relativistic physics. However, spin-orbit (SP) coupling is a notable exception, which arises from the relativistic Dirac equation of the electrons [1]. The emerging science of spintronics makes crucial use of the S-P coupling to manipulate electron spins by purely electric means. The proposed Datta-Das device [2] modulates the current flow through the spin procession caused by the SP coupling. More recently, Murakami, Nagaosa and Zhang [3,4] proposed a method of generating the dissipationless spin current by applying an electric field in the p-doped semiconductors. This effect and the similar proposal for the ndoped semiconductors [5] both make crucial use of the SP coupling. In contrast to the generation of the spin current by coupling to the ferromagnetic moment, purely electric manipulation has an intrinsic advantage. However, unlike the ferromagnetic moment, which can be spontaneously generated through the strong correlation of spins, the conventional wisdom states that the SP coupling is a non-interacting one-body effect, whose microscopic magnitude is fixed by the underlying relativistic physics.On the other hand, recent interests are revived on the Landau-Pomeranchuk (L-P) [6] fermi surface instabilities, largely in connection with electronic liquid crystal states with spontaneously broken rotational symmetry [7,8,9,10,11,12], and in connections with hidden orders in heavy fermion systems [13,14,15]. Varma's recent work showed that the L-P instability could lead to the opening of an anisotropic gap at the fermi surface [13]. In this paper, we show that the SP coupling can be generated dynamically in a non-relativistic system through strong correlation effects as the L-P instability in the spin channel with higher orbital angular momentum. It emerges collectively after a phase transition, which is continuously tunable either by temperature or by a quantum parameter at zero temperature. Unlike the ferromagnet, our ordered phase keeps time reversal symmetry. Also in contrast to the L-P instabilities considered by the majority of previous theories, most translationally invariant liquid phases in our model do not break rotational symmetry, and some of them preserve time reversal and parity symmetries...

Denice Feig and colleagues assess the association between gestational diabetes, gestational hypertension, and preeclampsia and the development of future diabetes in a database analysis of pregnant women in Ontario, Canada.