arXiv subjects

Xiao-Gang Wen

Publications and source records attributed to Xiao-Gang Wen.

At least 217 records · Page 12Linked to original sources

arXiv2003

Artificial light and quantum order in systems of screened dipoles

The origin of light is a unsolved mystery in nature. Recently, it was suggested that light may originate from a new kind of order - quantum order. To test this idea in experiments, we study systems of screened magnetic/electric dipoles in 2D and 3D lattices. We show that our models contain an artificial light -- a photon-like collective excitation. We discuss how to design realistic devices that realize our models. We show that the ``speed of light'' and the ``fine structure constant'' of the artificial light can be tuned in our models. The properties of artificial atoms (bound states of pairs of artificial charges) are also discussed. The existence of artificial light (as well as artificial electron) in condensed matter systems suggests that elementary particles, such as light and electron, may not be elementary. They may be collective excitations of quantum order in our vacuum. Our models further suggest that a gauge theory is a string-net theory in disguise. Light is a fluctuation of nets of large closed strings and charge is the end of open strings.

cond-mat.mes-hall↗

arXiv2003

Quantum order from string-net condensations and origin of light and massless fermions

Recently, it was pointed out that quantum orders and the associated projective symmetry groups can produce and protect massless gauge bosons and massless fermions in local bosonic models. In this paper, we demonstrate that a state with such kind of quantum orders can be viewed as a string-net condensed state. The emerging gauge bosons and fermions in local bosonic models can be regarded as a direct consequence of string-net condensation. The gauge bosons are fluctuations of nets of large closed strings which are condensed in the ground state. The ends of condensed open strings are the charged particles of the corresponding gauge field. For certain types of strings, the ends of strings can even be fermions. According to the string-net picture, fermions always carry gauge charges. This suggests the existence of a new discrete gauge field that couples to neutrinos and neutrons. We also discuss how chiral symmetry that protects massless Dirac fermions can emerge from the projective symmetry of quantum order.

hep-th↗

arXiv2002

Gauge invariance and electron spectral functions in underdoped cuprates

The single particle spectral function for the normal state of underdoped high $T_c$ cuprates is studied within the slave particle framework. We find that the presence of a massless dynamical gauge field - a direct consequence of the quantum order - explains the broad, but not totally incoherent, line-shapes observed in experiments. The issue of the negative anomalous dimension of a recently proposed gauge invariant single particle amplitude is also considered. We show how the anomalous behavior of the single particle amplitude can be incorporated within the slave particle approach and, thus reinterpreted, lead to physical phenomenology.

cond-mat.str-el↗

arXiv2002

Quantum orders in an exact soluble model

We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: $H=16g \sum_i S^y_i S^x_{i+x} S^y_{i+x+y} S^x_{i+y}$. We show that the ground states for $g<0$ and $g>0$ have different quantum orders described by Z2A and Z2B projective symmetry groups. The phase transition at $g=0$ represents a new kind of phase transitions that changes quantum orders but not symmetry. Both the Z2A and Z2B states are described by $Z_2$ lattice gauge theories at low energies. They have robust topologically degenerate ground states and gapless edge excitations.

quant-ph↗

arXiv2002

Spin-disordered superfluid state for spin-1 bosons with fractional spin and statistics

We study a strongly correlated spin-1 Bose gas in 2D space by using the projective construction. A spin-disordered superfluid state is constructed and proposed as a candidate competing with the conventional polar condensate when interaction is antiferromagnetic. This novel state has a non-trivial topological order whose low energy excitations carry fractional spin, charge, and statistics. The spin excitations become gapless only at the edge and are described by level-1 SU(2) Kac-Moody algebra. The edge state is identical to the edge state of the chiral spin liquid or the right moving sector of spin-1/2 chain.

cond-mat.str-el↗

arXiv2002

Gapless Fermions and Quantum Order

Using 2D quantum spin-1/2 model as a concrete example, we studied the relation between gapless fermionic excitations (spinons) and quantum orders in some spin liquid states. Using winding number, we find the projective symmetry group that characterizes the quantum order directly determines the pattern of Fermi points in the Brillouin zone. Thus quantum orders provide an origin for gapless fermionic excitations.

cond-mat.str-el↗

arXiv2002

Quantum Order: a Quantum Entanglement of Many Particles

It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum orders in free fermion systems and in 2D spin-1/2 systems. We generalize the Landau's theory for the classical orders and introduce projective symmetry group and Fermi surface topology to characterize different quantum orders.

cond-mat.str-el↗

arXiv2002

Spin correlations in the algebraic spin liquid - implications for high Tc superconductors

We propose that underdoped high $T_c$ superconductors are described by an algebraic spin liquid (ASL) at high energies, which undergoes a spin-charge recombination transition at low energies. The spin correlation in the ASL is calculated via its effective theory - a system of massless Dirac fermions coupled to a U(1) gauge field. We find that without fine tuning any parameters the gauge interaction strongly enhances the staggered spin correlation even in the presence of a large single particle pseudo-gap. This allows us to show that the ASL plus spin-charge recombination picture can explain many highly unusual properties of underdoped high $T_c$ superconductors.

cond-mat.str-el↗

arXiv2002

Quantum Orders and Symmetric Spin Liquids

A concept -- quantum order -- is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize universality classes of quantum states (described by {\em complex} ground state wave-functions) is much richer then classical orders that characterize universality classes of finite temperature classical states (described by {\em positive} probability distribution functions). The Landau's theory for orders and phase transitions does not apply to quantum orders since they cannot be described by broken symmetries and the associated order parameters. We find projective representations of symmetry groups (which will be called projective symmetry groups) can be used to characterize quantum orders. With the help of quantum orders and the projective symmetry groups, we construct hundreds of symmetric spin liquids, which have SU(2), U(1) or $Z_2$ gauge structures at low energies. Remarkably, some of the stable quantum phases support gapless excitations even without any spontaneous symmetry breaking. We propose that it is the quantum orders (instead of symmetries) that protect the gapless excitations and make algebraic spin liquids and Fermi spin liquids stable. Since high $T_c$ superconductors are likely to be described by a gapless spin liquid, the quantum orders and their projective symmetry group descriptions lay the foundation for spin liquid approach to high $T_c$ superconductors.

cond-mat.str-el↗

arXiv2001

Origin of Light

The existence of light (a massless U(1) gauge boson) is one of unresolved mysteries in nature. In this paper, we would like to propose that light is originated from certain quantum orders in our vacuum. We will construct quantum models on lattice to demonstrate that some quantum orders can give rise to light without breaking any symmetries and without any fine tuning. Through our models, we show that the existence of light can simply be a phenomenon of quantum coherence in a system with many degrees of freedom. Massless gauge fluctuations appears commonly and naturally in strongly correlated systems.

hep-th↗

arXiv2001

Signature of the staggered flux state around a superconducting vortex in underdoped cuprates

Based on the SU(2) lattice gauge theory formulation of the t-J model, we discuss possible signature of the unit cell doubling associated with the staggered flux (SF) state in the lightly doped spin liquid. Although the SF state appears only dynamically in a uniform d-wave superconducting (SC) state, a topological defect [SU(2) vortex] freezes the SF state inside the vortex core. Consequently, the unit cell doubling shows up in the hopping ($χ_{ij}$) and pairing ($Δ_{ij}$) order parameters of physical electrons. We find that whereas the center in the vortex core is a SF state, as one moves away from the core center, a correlated staggered modulation of $χ_{ij}$ and $Δ_{ij}$ becomes predominant. We predict that over the region outside the core and inside the internal gauge field penetration depth around a vortex center, the local density-of-states (LDOS) exhibits staggered peak-dip (SPD) structure inside the V-shaped profile when measured on the bonds. The SPD structure has its direct origin in the unit cell doubling associated with the SF core and the robust topological texture, which has little to do with the symmetry of the d-wave order parameter. Therefore the structure may survive the tunneling matrix element effects and easily be detected by STM experiment.

cond-mat.str-el↗

arXiv2001

Critical points in edge tunneling between generic FQH states

A general description of weak and strong tunneling fixed points is developed in the chiral-Luttinger-liquid model of quantum Hall edge states. Tunneling fixed points are a subset of `termination' fixed points, which describe boundary conditions on a multicomponent edge. The requirement of unitary time evolution at the boundary gives a nontrivial consistency condition for possible low-energy boundary conditions. The effect of interactions and random hopping on fixed points is studied through a perturbative RG approach which generalizes the Giamarchi-Schulz RG for disordered Luttinger liquids to broken left-right symmetry and multiple modes. The allowed termination points of a multicomponent edge are classified by a B-matrix with rational matrix elements. We apply our approach to a number of examples, such as tunneling between a quantum Hall edge and a superconductor and tunneling between two quantum Hall edges in the presence of interactions. Interactions are shown to induce a continuous renormalization of effective tunneling charge for the integrable case of tunneling between two Laughlin states. The correlation functions of electronlike operators across a junction are found from the B matrix using a simple image-charge description, along with the induced lattice of boundary operators. Many of the results obtained are also relevant to ordinary Luttinger liquids.

cond-mat.mes-hall↗

arXiv2001

Electron spectral function and algebraic spin liquid for the normal state of underdoped high $T_c$ superconductors

We propose to describe the spin fluctuations in the normal state of underdoped high $T_{c}$ superconductors as a manifestation of an algebraic spin liquid. We have performed calculations within the slave-boson model to support our proposal. Under the spin-charge separation picture, the normal state (the spin-pseudogap phase) is described by massless Dirac fermions, charged bosons, and a gauge field. We find that the gauge interaction is a marginal perturbation and drives the mean-field free-spinon fixed point to a more complicated spin-quantum-fixed-point -- the algebraic spin liquid, where gapless excitations interact at low energies. The electron spectral function in the normal state was found to have a Luttinger-liquid-like line shape as observed in experiments. The spectral function obtained in the superconducting state shows how a coherent quasiparticle peak appears from the incoherent background as spin and charge recombine.

cond-mat.supr-con↗

arXiv2001

Striped States in Quantum Hall Effect: Deriving a Low Energy Theory from Hartree-Fock

There is growing experimental and theoretical evidence that very clean two dimensional electron systems form unidirectional charge density waves (UCDW) or ``striped'' states at low temperatures and at Landau level filling fractions of the form nu = M + x with 4 < M < 10 an integer and 0.4 < x < 0.6. Following previous work, we model the striped state using a Hartree-Fock approach. We construct the low energy excitations of the system by making smooth deformations of the stripe edges analogous to the construction of edge state excitations of quantum Hall droplets. These low energy excitations are described as a coupled Luttinger liquid theory, as discussed previously by MacDonald and Fisher (PRB61 5724 2000). Here, we extend that work and explicitly derive all of the parameters of this low energy theory using a Hartree Fock approach. We also make contact with the equivalent low energy hydrodynamic approach of Fogler and Vinokur (PRL84 5828 2000) and similarly derive the parameters of this theory. As examples of the use of these results, we explicitly calculate the low-energy excitation spectrum and study tunneling into the striped state.

cond-mat.mes-hall↗

arXiv2001

Staggered local density-of-states around the vortex in underdoped cuprates

We have studied a single vortex with the staggered flux (SF) core based on the SU(2) slave-boson theory of high $T_c$ superconductors. We find that whereas the center in the vortex core is a SF state, as one moves away from the core center, a correlated staggered modulation of the hopping amplitude $χ$ and pairing amplitude $Δ$ becomes predominant. We predict that in this region, the local density-of-states (LDOS) exhibits staggered modulation when measured on the bonds, which may be directly detected by STM experiments.

cond-mat.str-el↗

arXiv2000

Tunneling density of states of high T_c superconductors d-wave BCS model vs. SU(2) slave boson model

Motivated by recent experimental measurements of the tunneling characteristics of high T_{c} materials using scanning tunneling spectroscopy, we have calculated the IV and differential conductance curves in the superconducting state at zero temperature. Comparing the two results obtained via BCS-like d-wave pairing and the SU(2) slave boson approach, we find that the slave-boson model can explain the asymmetric background observed in experiments. The slave-boson model also predicts that the height of the conductance peak relative to the background is proportional to the hole doping concentration $x$, at least for under-doped samples. We also observe the absence of the van Hove singularity, and comment on possible implications.

cond-mat.str-el↗

arXiv2000

Vortex Structure in Underdoped Cuprates

In underdoped cuprates the normal state is highly anomalous and is characterized as a pseudogap phase. The question of how to describe the ``normal'' core of a superconducting vortex is an outstanding open problem. We show that the SU(2) formulation of the t-J model provides a description of the normal state as well as the vortex core. Interestingly, the pseudogap persists inside the core. We also found that it is likely that the core consists of a state which breaks translational symmetry due to the existence of staggered current which generate staggered magnetic field with very slow dynamics. This staggered flux state is likely to be the ground state for magnetic fields higher than $H_{c2}$. Experiments to test this picture are proposed.

cond-mat.str-el↗

arXiv2000

Anomalous magnetic splitting of the Kondo resonance

The splitting of the Kondo resonance in the density of states of an Anderson impurity in finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for nonzero magnetic field and Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulae are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large-N approaches to spin-1/2 impurities at finite magnetic field is suggested.

cond-mat.str-el↗