arXiv subjects

Cenke Xu

Publications and source records attributed to Cenke Xu.

At least 145 records · Page 8Linked to original sources

arXiv2012

Unconventional Quantum Critical Points

In this paper we review the theory of unconventional quantum critical points that are beyond the Landau's paradigm. Three types of unconventional quantum critical points will be discussed: (1). The transition between topological order and semiclassical spin ordered phase; (2). The transition between topological order and valence bond solid phase; (3). The direct second order transition between different competing orders. We focus on the field theory and universality class of these unconventional quantum critical points. Relation of these quantum critical points with recent numerical simulations and experiments on quantum frustrated magnets are also discussed.

cond-mat.str-el↗

arXiv2012

Topological Quantum Liquids with Quaternion Non-Abelian Statistics

Noncollinear magnetic order is typically characterized by a "tetrad" ground state manifold (GSM) of three perpendicular vectors or nematic-directors. We study three types of tetrad orders in two spatial dimensions, whose GSMs are SO(3) = S^3/Z_2, S^3/Z_4, and S^3/Q_8, respectively. Q_8 denotes the non-Abelian quaternion group with eight elements. We demonstrate that after quantum disordering these three types of tetrad orders, the systems enter fully gapped liquid phases described by Z_2, Z_4, and non-Abelian quaternion gauge field theories, respectively. The latter case realizes Kitaev's non-Abelian toric code in terms of a rather simple spin-1 SU(2) quantum magnet. This non-Abelian topological phase possesses a 22-fold ground state degeneracy on the torus arising from the 22 representations of the Drinfeld double of Q_8.

cond-mat.str-el↗

arXiv2011

Nematic orders in Iron-based superconductors

In the newly discovered iron-based superconductors, many experiments have demonstrated the existence of the rotational symmetry breaking nematic order, which has been a prevailing phenomenon in many correlated electronic systems. In this paper, we review nematic behaviors in iron-pnictides and the mechanism behind the development of the nematic order. We discuss evidences that support the spin-driven nematicity in iron-pnictides. Theories, results and predictions will be discussed based on this picture. We also briefly discuss the generalization of this theory to the nematicity in iron-chalcogenides.

cond-mat.str-el↗

arXiv2011

Two-orbital Schwinger Boson Representation of Spin-One: Application to a Non-abelian Spin Liquid with Quaternion Gauge Field

A non-abelian spin liquid in triangular lattice spin-1 systems was recently formulated in the form of continuum field theory [T. Grover, and T. Senthil, Phys. Rev. Lett. 107, 077203 (2011); Cenke Xu, A.W.W. Ludwig, arXiv:1012.5671]. It has spin-1/2 bosonic spinons coupled to emergent quaternion gauge fields, and can be obtained by quantum disordering a non-collinear spin nematic order hypothesized to describe NiGa_2S_4 [H. Tsunetsugu, and M. Arikawa, J. Phys. Soc. Jpn. 75, 083701 (2006)], However a microscopic lattice description, e.g. the lattice spinon (mean-field) Hamiltonian and the spin wavefunction, has been missing, and it has been noted that the standard Schwinger boson or bosonic triplon representations of spin-1 cannot describe this spin liquid. In this paper a two-orbital Schwinger boson representation for spin-1 systems is developed and used to construct a mean-field description of this quaternion spin liquid. Projecting the mean-field state produces a prototype wavefunction, which is a superposition of close-packed AKLT loop configurations with nontrivial amplitudes. This new formalism and related wavefunctions may be generalized to higher spin systems and can possibly produce spin liquid states with even richer emergent gauge structures.

cond-mat.str-el↗

arXiv2011

Spin Liquid Phases for Spin-1 systems on the Triangular lattice

Motivated by recent experiments on material Ba3NiSb2O9, we propose two novel spin liquid phases (A and B) for spin-1 systems on a triangular lattice. At the mean field level, both spin liquid phases have gapless fermionic spinon excitations with quadratic band touching, thus in both phases the spin susceptibility and C_v/T saturate to a constant at zero temperature, which are consistent with the experimental results on Ba3NiSb2O9. On the lattice scale, these spin liquid phases have Sp(4) ~ SO(5) gauge fluctuation; while in the long wavelength limit this Sp(4) gauge symmetry is broken down to U(1)xZ_2 in type A spin liquid phase, and broken down to Z_4 in type B phase. We also demonstrate that the $A$ phase is the parent state of the ferro-quadrupole state, nematic state, and the noncollinear spin density wave state.

cond-mat.str-el↗

arXiv2011

High pressure sequence of Ba_3NiSb_2O_9 structural phases: new $S = 1$ quantum spin-liquids based on Ni^{2+}

By using a high pressure, high temperature (HPHT) technique, the antiferromagnetically ordered ($T_N$ = 13.5 K) 6H-A phase of Ba$_3$NiSb$_2$O$_9$ was transformed into two new gapless quantum spin liquid(QSL) candidates with S=1 (Ni$^{2+}$) moments: the 6H-B phase with a Ni$^{2+}$-triangular lattice and the 3C-phase with a Ni$^{2+}$-three-dimensional (3D) edge-shared tetrahedral lattice. Both compounds show no magnetic order down to 0.35 K despite Curie-Weiss temperatures $θ_{CW}$ of -75.5 K (6H-B) and -182.5 K (3C), respectively. Below $\sim 25$ K the magnetic susceptibility of the 6H-B phase saturates to a constant value $χ_0 = 0.013 $ emu/mol which is followed below 7 K, by a linear-temperature dependent magnetic specific heat ($C_M$) displaying a giant coefficient $γ$ = 168 mJ/mol-K$^2$. Both observations suggest the development of a Fermi-liquid like ground state characterized by a Wilson ratio of 5.6 in this insulating material. For the 3C phase, the $C_M \propto T^2$ behavior indicates a unique S=1, 3D QSL ground-state.

cond-mat.str-el↗

arXiv2011

Phase Diagram of the Kane-Mele-Hubbard model

Motivated by recent numerical results, we study the phase diagram of the Kane-Mele-Hubbard (KHM) model, especially the nature of its quantum critical points. The phase diagram of the Kane-Mele-Hubbard model can be understood by breaking the SO(4) symmetry of our previous work down to U(1)_spin x U(1)_charge x PH symmetry. The vortices of the inplane Neel phase carry charge, and the proliferation of the charged magnetic vortex drives the transition between the inplane Neel phase and the QSH insulator phase; this transition belongs to the 3d XY universality class. The transition between the liquid phase and the inplane Neel phase is an anisotropic O(4) transition, which eventually becomes first order due to quantum fluctuation. The liquid-QSH transition is predicted to be first order based on a 1/N calculation.

cond-mat.str-el↗

arXiv2011

Quantum Phase Transitions around the Staggered Valence Bond Solid

Motivated by recent numerical results, we study the quantum phase transitions between Z_2 spin liquid, Neel ordered, and various valence bond solid (VBS) states on the honeycomb and square lattices, with emphasis on the staggered VBS. In contrast to the well-understood columnar VBS order, the staggered VBS is not described by an XY order parameter with Z_N anisotropy close to these quantum phase transitions. Instead, we demonstrate that on the honeycomb lattice, the staggered VBS is more appropriately described as an O(3) or CP(2) order parameter with cubic anisotropy, while on the square lattice it is described by an O(4) or CP(3) order parameter.

cond-mat.str-el↗

arXiv2011

Entanglement Entropy of Coupled Conformal Field Theories and Fermi Liquids

In this paper we calculate the entanglement entropy of two coupled gapless systems in general spatial dimension d. The gapless systems can be either conformal field theories (CFT), or Fermi liquids. We assume the two systems are coupled uniformly in a h-dimensional submanifold of the space, with 0 <= h <= d. We will focus on the scaling of the entanglement entropy with the size of the system, and its scaling with the inter-system coupling constant g. Three approaches will be used for our calculation: (1) exact calculation with ground state wave-functional, (2) perturbative calculation with functional path integral, (3) scaling argument.

cond-mat.str-el↗

arXiv2010

Majorana liquids: the complete fractionalization of the electron

We describe ground states of correlated electron systems in which the electron fractionalizes into separate quasiparticles which carry its spin and its charge, and into real Majorana fermions which carry its Fermi statistics. Such parent states provide a unified theory of previously studied fractionalized states: their descendants include insulating and conducting states with neutral spin S=1/2 fermionic spinons, and states with spinless fermionic charge carriers. We illustrate these ideas on the honeycomb lattice, with field theories of such states and their phase transitions.

cond-mat.str-el↗

arXiv2010

Geometric phases and competing orders in two dimensions

We discuss the problem of characterizing "quantum disordered" ground states, obtained upon loss of antiferromagnetic order on general lattices in two spatial dimensions, with arbitrary electronic band structure. A key result is the response in electron bilinears to the skyrmion density in the local antiferromagnetic order, induced by geometric phases. We also discuss the connection to topological terms obtained under situations where the electronic spectrum has a Dirac form.

cond-mat.str-el↗

arXiv2010

Quantum Spin Hall, triplet Superconductor, and topological liquid on the honeycomb lattice

We classify the order parameters on the honeycomb lattice using the SO(4) symmetry of the Hubbard model. We will focus on the topologically nontrivial quantum spin Hall order and spin triplet superconductor, which together belong to the (3, 3) representation of the SO(4). Depending on the microscopic parameters, this (3, 3) order parameter has two types of ground states with different symmetries: type A, the ground state manifold is [S^2xS^2]/Z_2; and type B, with ground state manifold SO(3)xZ_2. We demonstrate that phase A is adjacent to a Z_2xZ_2 topological phase with mutual semion statistics between spin and charge excitations, while phase B is adjacent to a nonabelian phase described by SU(2) Chern-Simons theory. Connections of our study to the recent quantum Monte Carlo simulation on the Hubbard model on the honeycomb lattice will also be discussed.

cond-mat.str-el↗

arXiv2010

Fractionalization in Superconductor Josephson Junction Arrays Hinged by Quantum Spin Hall edges

In this paper we study a novel superconductor-ferromagnet-superconductor (SC-FM-SC) Josephson junction array deposited on top of a two-dimensional quantum spin Hall (QSH) insulator. The existence of Majorana bound states at the interface between SC and FM gives rise to charge-e tunneling, in addition to the usual charge-2e Cooper pair tunneling, between neighboring superconductor islands. Moreover, because Majorana fermions encode the information of charge number parity, an exact Z_2 gauge structure naturally emerges and leads to many new insulating phases, including a deconfined phase where electrons fractionalize into charge-e bosons and topological defects. A new superconductor-insulator transition has also been found.

cond-mat.stat-mech↗

arXiv2010

Liquids in multi-orbital SU(N) Magnets with Ultracold Alkaline Earth Atoms

In this work we study one family of liquid states of k-orbital SU(N) spin systems, focusing on the case of k = 2 which can be realized by ultracold alkaline earth atoms trapped in optical lattices, with N as large as 10. Five different algebraic liquid states with selectively coupled charge, spin and orbital quantum fluctuations are considered. The algebraic liquid states can be stabilized with large enough N, and the scaling dimension of physical order parameters is calculated using a systematic 1/N expansion. The phase transitions between these liquid states are also studied, and all the algebraic liquid states discussed in this work can be obtained from one "mother" state with SU(2) x U(1) gauge symmetry.

cond-mat.str-el↗

arXiv2010

Emergent Gravity at a Lifshitz Point from a Bose Liquid on the Lattice

We propose a model with quantum bosons on the fcc lattice, which has a stable algebraic Bose liquid phase at low energy. We show that this phase is described by emergent quantum gravity at the Gaussian z = 3 Lifshitz fixed point in 3+1 dimensions. The stability of this algebraic Bose liquid phase is guaranteed by the gauge symmetry of gravitons and self-duality of the low energy field theory. By tuning one parameter in the lattice boson model we can drive a phase transition between the z = 3 Lifshitz gravity and another algebraic Bose liquid phase, described by gravity at the z = 2 Lifshitz point.

hep-th↗

arXiv2010

Classical Phase Transitions of Geometrically Constrained O($N$) Spin Systems

We study the phase transition between the high temperature algebraic liquid phase and the low temperature ordered phase in several different types of locally constrained O(N) spin systems, using a unified constrained Ginzburg-Landau formalism. The models we will study include: 1, O(N) spin-ice model with cubic symmetry; 2, O(N) spin-ice model with easy-plane and easy-axis anisotropy; 3, a novel O(N) "spin-plaquette" model, with a very different local constraint from the spin-ice. We calculate the renormalization group equations and critical exponents using a systematic ε= 4 - d expansion with constant N, stable fixed points are found for large enough N. In the end we will also study the situation with softened constraints, the defects of the constraints will destroy the algebraic phase and play an important role at all the transitions.

cond-mat.stat-mech↗

arXiv2010

Quantum critical points of Helical Fermi Liquids

Following our previous work, we study the quantum phase transitions which spontaneously develop ferromagnetic spin order in helical fermi liquids which breaks continuous spin-space rotation symmetry, with application to the edge states of 3d topological band insulators. With finite fermi surface, the critical point has both z = 3 over-damped and z = 2 propagating quantum critical modes, and the z = 3 mode will lead to non-fermi liquid behavior on the entire fermi surface. In the ordered phase, the Goldstone mode is over-damped unless it propagates along special directions, and quasiparticle is ill defined on most parts of the fermi surface except for special points. Generalizations of our results to other systems with spin-orbit couplings are also discussed.

cond-mat.str-el↗

arXiv2010

Time-Reversal Phase Transition at the Edge of 3d Topological Band Insulator

We study the time reversal (T) symmetry breaking of 2d helical fermi liquid, with application to the edge states of 3d topological band insulators with only one two-component Dirac fermion at finite chemical potential, as well as other systems with spin-orbit coupling. The T-breaking Ising order parameter is not over-damped and the theory is different from the ordinary Hertz-Millis theory for order parameters at zero momentum. We argue that the T-breaking phase transition is an 3d Ising transition, and the quasiparticles are well-defined in the quantum critical regime.

cond-mat.str-el↗