arXiv subjects

Lorenz Bartosch

Publications and source records attributed to Lorenz Bartosch.

34 records · Page 2Linked to original sources

arXiv2005

Competing Orders and non-Landau-Ginzburg-Wilson Criticality in (Bose) Mott transitions

This paper reviews a recent non-Landau-Ginzburg-Wilson (LGW) approach to superfluid to Mott insulator transitions in two dimensional bosonic lattice systems, using a dual vortex field theory (cond-mat/0408329). The physical interpretation of conventional LGW theory of quantum criticality is re-examined and similarities and differences with the vortex picture are discussed. The ``unification'' of various competing (insulating) orders, and the coincidence of these orders with the Mott transition are readily understood in this formulation. Some aspects of the recent theory of ``deconfined'' quantum criticality, which are to an extent subsumed in this approach, are discussed. A pedagogical presentation of the ``nuts and bolts'' of boson-vortex duality at the hamiltonian level is included, tailored to a condensed matter audience.

cond-mat.str-el↗

arXiv2005

Putting competing orders in their place near the Mott transition

We describe the localization transition of superfluids on two-dimensional lattices into commensurate Mott insulators with average particle density p/q (p, q relatively prime integers) per lattice site. For bosons on the square lattice, we argue that the superfluid has at least q degenerate species of vortices which transform under a projective representation of the square lattice space group (a PSG). The formation of a single vortex condensate produces the Mott insulator, which is required by the PSG to have density wave order at wavelengths of q/n lattice sites (n integer) along the principle axes; such a second-order transition is forbidden in the Landau-Ginzburg-Wilson framework. We also discuss the superfluid-insulator transition in the direct boson representation, and find that an interpretation of the quantum criticality in terms of deconfined fractionalized bosons is only permitted at special values of q for which a permutative representation of the PSG exists. We argue (and demonstrate in detail in a companion paper: L. Balents et al., cond-mat/0409470) that our results apply essentially unchanged to electronic systems with short-range pairing, with the PSG determined by the particle density of Cooper pairs. We also describe the effect of static impurities in the superfluid: the impurities locally break the degeneracy between the q vortex species, and this induces density wave order near each vortex. We suggest that such a theory offers an appealing rationale for the local density of states modulations observed by Hoffman et al. (cond-mat/0201348) in STM studies of the vortex lattice of BSCCO, and allows a unified description of the nucleation of density wave order in zero and finite magnetic fields. We note signatures of our theory that may be tested by future STM experiments.

cond-mat.str-el↗

arXiv2005

Competing orders II: the doped quantum dimer model

We study the phases of doped spin S=1/2 quantum antiferromagnets on the square lattice, as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at zero doping, to superconductors at moderate doping. The interplay between density wave/VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0 sector. We extend the dimer model to include fermionic S=1/2 excitations, and show that its mean-field, static gauge field saddle points have projective symmetries (PSGs) similar to those of `slave' particle U(1) and SU(2) gauge theories. We account for the non-perturbative effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper (L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1 excitations and their coupling to superflow and density wave fluctuations.

cond-mat.str-el↗

arXiv2003

Optical conductivity of a quasi-one-dimensional system with fluctuating order

We describe a formally exact method to calculate the optical conductivity of a one-dimensional system with fluctuating order. For classical phase fluctuations we explicitly determine the optical conductivity by solving two coupled Fokker-Planck equations numerically. Our results differ considerably from perturbation theory and in contrast to Gaussian order parameter fluctuations show a strong dependence on the correlation length.

cond-mat.str-el↗

arXiv2003

Non-Fermi liquid behavior of quasi one-dimensional pseudogap materials

We study the spectral function of the pseudogap phase of quasi one-dimensional charge density wave materials. Using a stochastic approach and emphasizing an exact treatment of non-Gaussian order parameter fluctuations we will go beyond a usual perturbative calculation. Our results give a good fit to ARPES data and explain the absence of the Fermi edge in charge density wave materials even above the Peierls transition, indicating non-Fermi liquid behavior.

cond-mat.str-el↗

arXiv2002

Ferromagnetic Luttinger Liquids

We study weak itinerant ferromagnetism in one-dimensional Fermi systems using perturbation theory and bosonization. We find that longitudinal spin fluctuations propagate ballistically with velocity v_m << v_F, where v_F is the Fermi velocity. This leads to a large anomalous dimension in the spin-channel and strong algebraic singularities in the single-particle spectral function and in the transverse structure factor for momentum transfers q ~ 2 Delta/v_F, where 2 Delta is the exchange splitting.

cond-mat.str-el↗

arXiv2002

Dynamic scaling in the vicinity of the Luttinger liquid fixed point

We calculate the single-particle spectral function A (k, omega) of a one-dimensional Luttinger liquid by means of a functional renormalization group (RG) approach. Given an infrared energy cutoff Lambda = Lambda_0 e^{- l}, our approach yields the spectral function in the scaling form, A_Λ (k_F + p, omega) = tau Z_l tilde{A}_l (p xi, omega tau), where k_F is the Fermi momentum, Z_l is the wave-function renormalization factor, tau = 1 / Λis the time scale and xi = v_F / Λis the length scale associated with Lambda. At the Luttinger liquid fixed point (l rightarrow infty) our RG result for A (k, omega) exhibits the correct anomalous scaling properties, and for k = \pm k_F agrees exactly with the well-known bosonization result at weak coupling. Our calculation demonstrates that the field rescaling is essential for obtaining the crossover from Fermi liquid behavior to Luttinger liquid behavior from a truncation of the hierarchy of exact RG flow equations as the infrared cutoff is reduced.

cond-mat.str-el↗

arXiv2001

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies omega smaller than the inverse elastic life-time. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln^2-singularities in the DOS nu (omega) but only ln-singularities in the conductivity sigma(omega), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If lim_{omega -> 0} sigma (omega) > 0, then a metallic Coulomb gap nu(omega) propto |omega|/e^4 appears in the DOS at T=0 for frequencies below a certain crossover frequency Omega_2 which depends on the value of the DC conductivity sigma(0). Here, -e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find nu(omega) propto (|omega|/Omega_1)^{1/2} exp(-Omega_1/|omega|) at T = 0, where Omega_1 is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments.

cond-mat.str-el↗

arXiv2001

Fluctuation effects in disordered Peierls systems

We review the density of states and related quantities of quasi one-dimensional disordered Peierls systems in which fluctuation effects of a backscattering potential play a crucial role. The low-energy behavior of non-interacting fermions which are subject to a static random backscattering potential will be described by the fluctuating gap model (FGM). Recently, the FGM has also been used to explain the pseudogap phenomenon in high-$T_c$ superconductors. After an elementary introduction to the FGM in the context of commensurate and incommensurate Peierls chains, we develop a non-perturbative method which allows for a simultaneous calculation of the density of states (DOS) and the inverse localization length. First, we recover all known results in the limits of zero and infinite correlation lengths of the random potential. Then, we attack the problem of finite correlation lengths. While a complex order parameter, which describes incommensurate Peierls chains, leads to a suppression of the DOS, i.e. a pseudogap, the DOS exhibits a singularity at the Fermi energy if the order parameter is real and therefore refers to a commensurate system. We confirm these results by calculating the DOS and the inverse localization length for finite correlation lengths and Gaussian statistics of the backscattering potential with unprecedented accuracy numerically. Finally, we consider the case of classical phase fluctuations which apply to low temperatures where amplitude fluctuations are frozen out. In this physically important regime, which is also characterized by finite correlation lengths, we present analytic results for the DOS, the inverse localization length, the specific heat, and the Pauli susceptibility.

cond-mat.str-el↗

arXiv2000

Exactly solvable toy model for the pseudogap state

We present an exactly solvable toy model which describes the emergence of a pseudogap in an electronic system due to a fluctuating off-diagonal order parameter. In one dimension our model reduces to the fluctuating gap model (FGM) with a gap Delta (x) that is constrained to be of the form Delta (x) = A e^{i Q x}, where A and Q are random variables. The FGM was introduced by Lee, Rice and Anderson [Phys. Rev. Lett. {\bf{31}}, 462 (1973)] to study fluctuation effects in Peierls chains. We show that their perturbative results for the average density of states are exact for our toy model if we assume a Lorentzian probability distribution for Q and ignore amplitude fluctuations. More generally, choosing the probability distributions of A and Q such that the average of Delta (x) vanishes and its covariance is < Delta (x) Delta^{*} (x^{prime}) > = Delta_s^2 exp[ {- | x - x^{\prime} | / ξ}], we study the combined effect of phase and amplitude fluctutations on the low-energy properties of Peierls chains. We explicitly calculate the average density of states, the localization length, the average single-particle Green's function, and the real part of the average conductivity. In our model phase fluctuations generate delocalized states at the Fermi energy, which give rise to a finite Drude peak in the conductivity. We also find that the interplay between phase and amplitude fluctuations leads to a weak logarithmic singulatity in the single-particle spectral function at the bare quasi-particle energies. In higher dimensions our model might be relevant to describe the pseudogap state in the underdoped cuprate superconductors.

cond-mat.str-el↗

arXiv2000

Classical Phase Fluctuations in Incommensurate Peierls Chains

In the pseudogap regime of one-dimensional incommensurate Peierls systems, fluctuations of the phase of the order parameter prohibit the emergence of long-range order and generate a finite correlation length. For classical phase fluctuations, we present exact results for the average electronic density of states, the mean localization length, the electronic specific heat and the spin susceptibility at low temperatures. Our results for the susceptibility give a good fit to experimental data.

cond-mat.str-el↗

arXiv1999

Exact Numerical Calculation of the Density of States of the Fluctuating Gap Model

We develop a powerful numerical algorithm for calculating the density of states rho(omega) of the fluctuating gap model, which describes the low-energy physics of disordered Peierls and spin-Peierls chains. We obtain rho(omega) with unprecedented accuracy from the solution of a simple initial value problem for a single Riccati equation. Generating Gaussian disorder with large correlation length xi by means of a simple Markov process, we present a quantitative study of the behavior of rho (omega) in the pseudogap regime. In particular, we show that in the commensurate case and in the absence of forward scattering the pseudogap is overshadowed by a Dyson singularity below a certain energy scale omega^{ast}, which we explicitly calculate as a function of xi.

cond-mat.str-el↗

arXiv1999

Algorithm for obtaining the gradient expansion of the local density of states and the free energy of a superconductor

We present an efficient algorithm for obtaining the gauge-invariant gradient expansion of the local density of states and the free energy of a clean superconductor. Our method is based on a new mapping of the semiclassical linearized Gorkov equations onto a pseudo-Schroedinger equation for a three-component wave-function psi(x), where one component is directly related to the local density of states. Because psi(x) satisfies a linear equation of motion, successive terms in the gradient expansion can be obtained by simple linear iteration. Our method works equally well for real and complex order parameter, and in the presence of arbitrary external fields. We confirm a recent calculation of the fourth order correction to the free energy by Kosztin, Kos, Stone and Leggett [Phys. Rev. B 58, 9365 (1998)], who obtained a discrepancy with an earlier result by Tewordt [Z. Phys. 180, 385 (1964)]. We also give the fourth order correction to the local density of states, which has not been published before.

cond-mat.supr-con↗

arXiv1999

Correlation functions of higher-dimensional Luttinger liquids

Using higher-dimensional bosonization, we study correlation functions of fermions with singular forward scattering. Following Bares and Wen [Phys. Rev. B 48, 8636 (1993)], we consider density-density interactions in d dimensions that diverge for small momentum transfers as q^{- eta} with eta = 2 (d-1). In this case the single-particle Green's function shows Luttinger liquid behavior. We discuss the momentum distribution and the density of states and show that, in contrast to d=1, in higher dimensions the scaling behavior cannot be characterized by a single anomalous exponent. We also calculate the irreducible polarization for q close to 2 k_F and show that the leading singularities cancel. We discuss consequences for the effect of disorder on higher-dimensional Luttinger liquids.

cond-mat.str-el↗

arXiv1999

Singularities and Pseudogaps in the Density of States of Peierls Chains

We develop a non-perturbative method to calculate the density of states (DOS) of the fluctuating gap model describing the low-energy physics of electrons on a disordered Peierls chain. For real order parameter field we calculate the DOS at the Fermi energy exactly as a functional of the disorder for a chain of finite length L. Averaging rho (0) with respect to a Gaussian probability distribution of the Peierls order parameter, we show that in the thermodynamic limit the average DOS at the Fermi energy diverges for any finite value of the correlation length above the Peierls transition. Pseudogap behavior emerges only if the Peierls order parameter is finite and sufficiently large.

cond-mat.str-el↗

arXiv1997

An Exactly Solvable Model of N Coupled Luttinger Chains

We calculate the exact Green function of a special model of N coupled Luttinger chains with arbitrary interchain hopping t_{perp}. The model is exactly solvable via bosonization if the interchain interaction does not fall off in the direction perpendicular to the chains. For any finite N we find Luttinger liquid behavior and explicitly calculate the anomalous dimension gamma^(N). However, the Luttinger liquid state does not preclude coherent interchain hopping. We also show that gamma^(N) -> 0 for N -> infinity, so that in the limit of infinitely many chains we obtain a Fermi liquid.

cond-mat.str-el↗