Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session U39: Non-Fermi Liquids and Spin Liquids |
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Sponsoring Units: DCMP Chair: Alexander Balatsky, LANL Room: LACC 514 |
Thursday, March 24, 2005 8:00AM - 8:12AM |
U39.00001: Numerical Evidences of Fractionalization in an Easy-Axis Two-Spin Heisenberg Antiferromagnet Donna Sheng, Leon Balents Based on exact numerical calculations, we show that the generalized Kagome spin model in the easy axis limit exhibits a spin liquid, topologically degenerate ground state over a broad range of phase space, including a point at which the model is equivalent to a Heisenberg model with purely two-spin exchange interactions. We present an (to our knowledge the first) explicit calculation of the gap (and dispersion) of ``vison'' excitations, and exponentially decaying spin and vison 2-point correlators. These are hallmarks of deconfined, fractionalized and gapped spinons. The nature of the phase transition from the spin-liquid state to a magnetic ordered state tuned by a negative four-spin ``potential'' term is also discussed in light of the low energy spectrum. These results greatly expand the range and the theoretical view of the spin-liquid phase in the vicinity of the RK exactly soluble point. Numerical indications of the spin-liquid phase in other spin models will also be discussed. [Preview Abstract] |
Thursday, March 24, 2005 8:12AM - 8:24AM |
U39.00002: Hydrodynamic description of correlations in Quantum Fluids Fabio Franchini, Alexander Abanov We employ field theory methods to study correlation functions of Spin Chains. We derive asymptotic behaviors of the correlators through a hydrodynamic formulation of the problem. In particular, we are interested in a correlator known as Emptiness Formation Probability (EFP), which measures the probability $P(n)$ of formation of an empty region of length $n$ in the quantum fluid at low temperature. The EFP in the leading order is found as the action of the instanton solution of hydrodynamic equations of motion. This hydrodynamic approach has already been applied in the study of a number of systems, for instance the XXZ Spin Chain, a Bose gas with delta repulsion and free 1D fermions. The EFP for the XY Spin Chain is asymptotically Gaussian in $n$ at the isotropic point and exponential in the anisotropic regime. We study the crossover between these two regimes by calculating the leading intermediate asymptotics of the EFP using a bosonization approach (linearized hydrodynamics). To study the subleading contributions to the EFP, we include gradient corrections to hydrodynamics and study quantum fluctuations around the saddle-point ``instanton'' solution. [Preview Abstract] |
Thursday, March 24, 2005 8:24AM - 8:36AM |
U39.00003: Probing the Pseudogap for an Algebraic Spin Liquid Michael Hermele, T. Senthil, Matthew P. A. Fisher Algebraic spin liquids [1] are two-dimensional Mott insulators where the spin sector is in an interacting critical state. One such state, the staggered-flux spin liquid, has been argued to play a key role in the pseudogap regime of the underdoped cuprate superconductors [2,3]. We find that the staggered-flux state supports a variety of slowly-fluctuating competing orders, unified by an emergent SU(4) symmetry. Among these orders are the Neel vector and the order parameter for a columnar valence- bond solid. This structure may have important observable consequences for the rather high-temperature physics of the pseudogap regime. 1. W. Rantner and X.-G. Wen, PRL 86, 3871 (2001). 2. X.-G. Wen and P. A. Lee, PRL 76, 503 (1996). 3. T. Senthil and P. A. Lee, cond-mat/0406066. [Preview Abstract] |
Thursday, March 24, 2005 8:36AM - 8:48AM |
U39.00004: Calogero-Sutherland model and Quantum Benjamin-Ono Equation Alexander G. Abanov, Paul B. Wiegmann Collective field theory for Calogero-Sutherland model represents particles with fractional statistics in terms of holomorphic bosonic field made out of the density and velocity fields. We identify an operator equation of motion for this bosonic field with a quantum deformation of a known classical Benjamin-Ono equation. The latter equation is integrable and the same is true for its quantum version. The inverse scattering transform for the classical Benjamin-Ono equation can be extended to its quantum analog. Soliton solutions of quantum Benjamin- Ono equation correspond to particle and hole excitations of Calogero- Sutherland model. [Preview Abstract] |
Thursday, March 24, 2005 8:48AM - 9:00AM |
U39.00005: Berry phases emerging from the $\pi$-flux state Akihiro Tanaka, Xiao Hu We derive a new effective action describing fluctuations around the Affleck-Marston $\pi$-flux mean-field solution of the 2d Heisenberg antiferromagnet. The 5-dimensional Clifford algebra inherent in the Dirac fermion obtained as the continuum limit of the $\pi$-flux state is found to sustain a bulit-in competition between antiferromagnet (AF) and valence-bond-solid (VBS) orders. This naturally leads us to cast both orderings as components of a 5 component vectorial field $v$, for which we obtain an O(5) nonlinear sigma model with a novel Wess- Zumino (WZ) term proportional to the Mauer-Cartan form $\int_0^1 dt\int d^3 x v dv \wedge dv \wedge dv \wedge dv$, with $t\in[0,1]$ an auxiliary variable which extends $v(x)$ to $v(t,x)$ in such a way that $v(t=0,x)\equiv(0,0,0,0,1)$ and $v(t=1,x)\equiv v(x)$ are satisfied. We study properties of Berry phases extracted from this WZ term, and recover in particular the AF hedgehog Berry phases (with a VBS core) which are central to recent studies on 2D spin liquids. [Preview Abstract] |
Thursday, March 24, 2005 9:00AM - 9:12AM |
U39.00006: Rectification in quantum wires with strong electron interactions Bernd Braunecker, D.E. Feldman, J.B. Marston We investigate the rectification of a low-frequency ac bias in quantum wires with strong electron interactions in the presence of a localized asymmetric scattering potential. Electrons of opposite spin form a two-channel Luttinger liquid. We show that the $I-V$ curve significantly differs from that of the one-channel quantum wire\footnote{D. E. Feldman, S. Scheidl, and V. M. Vinokur, \urllink{cond-mat/0410089}{http://arxiv.org/abs/cond-mat/0410089}.} with polarized electrons. The dc current exhibits a non-monotonic dependence on the ac voltage bias, and the dc $I-V$ curve is strongly asymmetric at low voltages. [Preview Abstract] |
Thursday, March 24, 2005 9:12AM - 9:24AM |
U39.00007: A Tale of Two Theories: Quantum Griffiths Effects in Metallic Systems Antonio Castro Neto, Barbara Jones We show that two apparently contradictory theories on the existence of Griffiths-McCoy singularities in magnetic metallic systems are in fact mathematically equivalent. We discuss the generic phase diagram of the problem and show that there is a non-universal crossover temperature range T* $<$ T where power law behavior (Griffiths-McCoy behavior) is expect. For T $<$ T* power law behavior ceases to exist due to the destruction of quantum effects generated by the dissipation in the metallic environment. We show that T* is an analogue of the Kondo temperature and is controlled by non-universal couplings. [Preview Abstract] |
Thursday, March 24, 2005 9:24AM - 9:36AM |
U39.00008: Renormalization group study of bond order wave phase in the extended Hubbard chain Ka Ming Tam, Shan-Wen Tsai, David K. Campbell We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling. We obtain a finite region of bond charge density wave order near $U = 2V$ using one loop renormalization group (RG) method. We solve a long-standing controversy in this field, explaining why earlier standard g-ology calculations have not found this phase. We introduce a functional generalization of standard g-ology in which effects of the scattering processes involving electrons away from the Fermi points are included in a systematic way. We argue that this is an example in which formally irrelevant terms change the topology of the phase diagram. We discuss other scenarios in which this may occur and this generalized RG method is essential to fully characterize the phase diagram. [Preview Abstract] |
Thursday, March 24, 2005 9:36AM - 9:48AM |
U39.00009: Hole localization in Doped Mott Insulators Ting-pong Choy, Philip Phillips A key experimental puzzle surrounding the high-temperature copper oxide materials is the origin of the insulating behaviour in the underdoped regime. Using a self-consistent cluster method, we compute the resistivity of a lightly doped Mott insulator (described by the Hubbard model) using the Kubo formula in the one-loop approximation. We find that at high temperatures the resistivity increases as some power of temperature but at low temperatures diverges as $\exp(T_0/T)^s$ ($s\approx 0.66$) as is seen experimentally in the cuprates. The localization is due to the pseuedogap which is shown to be a ubiquitous feature of a doped Mott insulator. Quite generally, doped holes form magnetic polarons which remain localized in an otherwise antiferromagnetic background as a result of a non-perturbative phase shift. The phase shift is computed explicitly and is shown to vanish as $U\rightarrow \infty$, in agreement with the Nagaoka dilute limit. [Preview Abstract] |
Thursday, March 24, 2005 9:48AM - 10:00AM |
U39.00010: Variational study of triangular lattice Heisenberg spin-1/2 model with ring exchanges and spin liquid state in $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ Olexei Motrunich We study triangular lattice spin-1/2 system with antiferromagnetic Heisenberg and ring exchanges using variational approach focusing on possible realization of spin liquid states. Trial spin liquid wave functions are obtained by Gutzwiller projection of fermionic mean field states and their energetics is compared against magnetically ordered trial states. We find that in a range of ring exchange coupling upon destroying the antiferromagnetic order, the best such spin liquid state is essentially a Gutzwiller-projected Fermi sea state. We propose this spin liquid with spinon Fermi surface as a candidate for the nonmagnetic insulating phase observed in the organic compound $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$, and describe some experimental consequences of this proposal. [Preview Abstract] |
Thursday, March 24, 2005 10:00AM - 10:12AM |
U39.00011: The infrared catastrophe and tunneling into a correlated conductor Kelly Patton, Michael Geller It is well known that the tunneling density of states has anomalies (cusps, algebraic suppressions, and pseudogaps) at the Fermi energy in a wide variety of low- dimensional and strongly correlated electron systems. We propose that the origin of these anomalies is the infrared catastrophe associated with the sudden introduction of a new electron into a conductor during a tunneling event. We introduce an exact functional integral representation for the interacting Green's function, by means of a Hubbard-Stratonovich transformation, single out the field configurations responsible for the infrared catastrophe, and treat them with methods developed for the X-ray edge problem. Applications to a variety of interacting systems will be presented. [Preview Abstract] |
Thursday, March 24, 2005 10:12AM - 10:24AM |
U39.00012: Critical Theory of the Multi-Channel Anderson Impurity Model Henrik Johannesson, Carlos J. Bolech, Natan Andrei We have carried out a nonperturbative analysis of the multi-channel Anderson impurity model, using a combination of Bethe Ansatz and boundary conformal field theory techniques. We present exact, analytical expressions for the zero-temperature entropy, the low-temperature impurity thermodynamics - including the Wilson ratio - and the critical exponents of the Fermi edge singularities characterizing the time-dependent hybridization of conduction electrons and impurity. For the case of two channels we also present exact results for the single-electron Green's function, the impurity self-energy, and the low-temperature resistivity of the model. We compare our results to those obtained from more conventional, approximate methods. Implications for the study of the non-Fermi liquid physics of Uranium-based heavy fermion materials are discussed. [Preview Abstract] |
Thursday, March 24, 2005 10:24AM - 10:36AM |
U39.00013: Non-Fermi liquid behavior in a three-orbital Anderson model with inverted Hund's rule. Lorenzo De Leo, Michele Fabrizio We investigate the critical properties of a threefold orbitally degenerate Anderson impurity model in the presence of a generalized Hund's rule coupling. We use in combination conformal field theory and Wilson numerical renormalization group. The fixed points of the model correspond to boundary conformal field theories including spin, orbital and charge sectors together with a three state Potts model sector. Depending on the average occupation of the impurity we find different situations. In particular at particle-hole (p-h) symmetry we find an unstable non-Fermi liquid fixed point (UFP) separating a Kondo screened phase from a non-Fermi liquid stable phase. Away from p-h symmetry the non-Fermi liquid stable phase is replaced by a conventional Fermi liquid one but the UFP remains. The spectrum obtained numerically agrees with the finite size spectrum predicted by conformal field theory. We obtain the spectral function of the impurity across the UFP. Beyond the interest in the single impurity problem, this system can be relevant to understand via Dynamical Mean Filed Theory the behavior of a strongly correlated lattice model close to the Mott transition, where we expect that the UFP instability of the single impurity turns into a superconducting instability of the bulk. [Preview Abstract] |
Thursday, March 24, 2005 10:36AM - 10:48AM |
U39.00014: Quantum creep and variable range hopping of one-dimensional interacting electrons Thomas Nattermann The variable range hopping results for non-interacting electrons of Mott and Shklovskii are generalized to 1D disordered charge density waves and Luttinger liquids using an instanton approach. In the present paper we calculate the quantum creep of charges at zero temperature and the linear conductivity at finite temperatures for these systems. The hopping conductivity for the interacting electrons acquires the same form as for non-interacting particles if the one-particle density of states is replaced by the compressibility. It turns out that dissipation is crucial for tunneling to happen. Contrary to pure systems the new meta-stable state does not propagate through the system but is restricted to a region of the size of the tunneling region. This corresponds to the hopping of an integer number of charges over a finite distance. A global current results only if tunneling events fill the whole sample. We argue that rare events of extra low tunneling probability are not relevant for realistic systems of finite length. Finally we show that an additional Coulomb interaction only leads to small logarithmic corrections. [Preview Abstract] |
Thursday, March 24, 2005 10:48AM - 11:00AM |
U39.00015: Quasi-linear temperature dependence of the resistivity due to a nested Fermi surface Pedro Schlottmann Non-Fermi liquid (NFL) behavior is often found in the neighborhood of a quantum critical point (QCP). We consider a QCP arising from the nesting of Fermi surfaces of an electron pocket and a hole pocket separated by a wavevector ${\bf Q}$. The nesting gives rise to antiferromagnetism if the interaction between the carriers is repulsive. The order can gradually be suppressed by mismatching the nesting and a QCP is obtained as $T_N \to 0$. The specific heat $\gamma$ coefficient and the magnetic susceptibility increase with the logarithm of the temperature as $T$ is lowered.$^1$ The electrical resistivity and the linewidth of the neutron scattering quasi-elastic peak acquire a quasi-linear temperature dependence, as a consequence of the nesting of the Fermi surface.$^2$ This deviation from the usual Fermi liquid $T^2$ dependence is a manifestation of NFL behavior. The results are discussed in the context of NFL behavior observed in many heavy fermion compounds.$^3$ \vskip 0.1in \par\noindent Work supported by the National Science Foundation under grant No. DMR01-05431 and the Department of Energy under grant No. DE-FG02-98ER45797. \vskip 0.1in \par\noindent $^1$ P. Schlottmann, Phys. Rev. B {\bf 68}, 125105 (2003). \par\noindent $^2$ A. Virosztek and J. Ruvalds, Phys. Rev. B {\bf 42}, 4064 (1990). \par\noindent $^3$ G.R. Stewart, Rev. Mod. Phys. {\bf 73}, 797 (2001). [Preview Abstract] |
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U39.00016: Influence of thermal fluctuations on quantum phase transitions in 1D disordered systems: CDWs and Luttinger liquids Thomas Nattermann, Andreas Glatz The low temperature phase diagram of 1D weakly disordered quantum systems like charge or spin density waves and Luttinger liquids is studied by a \emph{full finite temperature} renormalization group (RG) calculation. For vanishing quantum fluctuations this approach is amended by an \emph{exact} solution in the case of strong disorder and by a mapping onto the \emph{Burgers equation with noise} in the case of weak disorder, respectively. At \emph{zero} temperature we reproduce the quantum phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At \emph{finite} temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wave length of the phason excitations. The existence of a zero temperature transition is reflected in a rich cross-over phase diagram of the correlation functions. In particular we find four different scaling regions: a \emph{classical disordered}, a \emph{quantum disordered}, a \emph{quantum critical} and a \emph{thermal} region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential. Applications to related systems are discussed as well. [Preview Abstract] |
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U39.00017: Nonlinear ac conductivity of interacting 1d electron systems Thomas Nattermann, Bernd Rosenow We consider low energy charge transport in one-dimensional (1d) electron systems with short range interactions under the influence of both periodic and random potentials. Combining RG and instanton methods, we calculate the nonlinear ac conductivity and discuss the crossover between the nonanalytic field dependence of the electric current at zero frequency and the linear ac conductivity at small electric fields and finite frequency. [Preview Abstract] |
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U39.00018: Breakdown of Strong Coupling Expansions for doped Mott Insulators Philip Phillips, Dimitrios Galanakis, Tudor Stanescu We show that doped Mott insulators, such as the copper-oxide superconductors, are asymptotically slaved in that the quasiparticle weight, $Z$, near half-filling depends critically on the existence of the high energy scale set by the upper Hubbard band. In particular, near half filling, the following dichotomy arises: $Z\ne 0$ when the high energy scale is integrated out but $Z=0$ in the thermodynamic limit when it is retained. Slavery to the high energy scale arises from quantum interference between electronic excitations across the Mott gap. [Preview Abstract] |
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U39.00019: Breakdown of One-Paramater Scaling in Quantum Critical Scenarios for the High-Temperature Copper-oxide Superconductors Philip Phillips, Claudio Chamon We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent, $z$, satisfies the unphysical constraint, $z<0$. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single correlation length scale is necessary to model transport in the cuprates. [Preview Abstract] |
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