arXiv subjects

Ian Affleck

Publications and source records attributed to Ian Affleck.

At least 109 records · Page 6Linked to original sources

arXiv2005

Junctions of three quantum wires

We study a junction of three quantum wires enclosing a magnetic flux. The wires are modeled as single-channel spinless Tomonaga-Luttinger liquids. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a non-trivial way. We study the problem using a mapping onto the dissipative Hofstadter model, describing a single particle moving on a plane in a magnetic field and a periodic potential coupled to a harmonic oscillator bath. Alternatively we study the problem by identifying boundary conditions corresponding to the low energy fixed points. We obtain a rich phase diagram including a chiral fixed point in which the asymmetric current flow is highly sensitive to the sign of the flux and a phase in which electron pair tunneling dominates. We also study the effects on the conductance tensor of the junction of contacting the three quantum wires to Fermi liquid reservoirs.

cond-mat.str-el↗

arXiv2005

Magnetic order and moment distribution in doped spin-chain systems

We consider the effect of doping on the magnetic order in quasi one-dimensional (1D) antiferromagnets. First the detailed magnetic response of finite spin-1/2 chains in the presence of a staggered field is determined, which by itself shows an interesting crossover as function of length and field strength. We can then understand the ordering by including an effective coupling between the chains, which results in a Neel ordered phase at low temperatures, but with a broad distribution of magnetic moments that has to be determined self-consistently.

cond-mat.str-el↗

arXiv2005

Luttinger liquid parameter for the spin-1 Heisenberg chain in a magnetic field

A recently derived general formula and older numerical results are combined to deduce the behavior of the transverse correlation exponent for the spin-1 Heisenberg antiferromagnetic chain in an applied magnetic field: eta = 1/2 - (2.0)m +O(m^2), where m is the magnetization per site. A comparison with the O(3) non-linear sigma-model is also made.

cond-mat.str-el↗

arXiv2005

Quantum vs. Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains

The competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chains is known to exhibit a 3-fold degenerate udu-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z_3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the 00u-type quantum plateau state (00= singlet dimer) is studied by bosonization, renormalization group and numerical diagonalization methods. The ground state phase diagram and the spin configuration in each phase are numerically determined. The translationally invariant Valence Bond Solid-type model with 4-spin and third neighbor interactions, which has the exact 00u-type quantum plateau state, is also presented. The phase transition to the classical udu-type ground state is also observed by varying the strength of 4-spin and third neighbor interactions. The relation between these two types of models with quantum plateau states is discussed.

cond-mat.str-el↗

arXiv2004

Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors

As a model of thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar superconductor. This problem can be mapped onto the physics of a Luttinger liquid of interacting bosons in 1 spatial dimension with a point impurity. When the applied magnetic field is tilted relative to the line defect, the corresponding quantum boson Hamiltonian is non-Hermitian. We analyze this problem using a combination of analytic and numerical (density matrix renormalization group) methods, uncovering a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field. Interactions allow a single columnar defect to be very effective in suppressing vortex tilt when the Luttinger liquid parameter g less than equal to 1.

cond-mat.supr-con↗

arXiv2004

Haldane-gap chains in a magnetic field

We consider quasi one dimensional spin-1 Heisenberg chains with crystal field anisotropy in a uniform magnetic field. We determine the dynamical structure factor in various limits and obtain a fairly complete qualitative picture of how it changes with the applied field. In particular, we discuss how the width of the higher energy single magnon modes depends on the field. We consider the effects of a weak interchain coupling. We discuss the relevance of our results for recent neutron scattering experiments on the quasi-1D Haldane-gap compound NDMAP.

cond-mat.str-el↗

arXiv2004

Non-Fermi liquid behavior in Kondo models

Despite the fact that the low energy behavior of the basic Kondo model cannot be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres and others to have a simple "local Fermi liquid theory" description. That is, electronic degrees of freedom become effectively non-interacting in the zero energy limit. However, generalized versions of the Kondo model involving more than one channel or impurity may exhibit low energy behavior of a less trivial sort which can, nonetheless, be solved exactly using either Bethe ansatz or conformal field theory and bosonization techniques. Now the low energy limit exhibits interacting many body behavior. For example, processes in which a single electron scatters off the impurity into a multi electron-hole state have a non-vanishing (and sometimes large) amplitude at zero energy. This corresponds to a rare solveable example of non-Fermi liquid behavior. Essential features of these phenomena are reviewed.

cond-mat.str-el↗

arXiv2004

The Kondo Screening Cloud around a Quantum Dot: Large-scale numerical Results

Measurements of the persistent current in a ring containing a quantum dot would afford a unique opportunity to finally detect the elusive Kondo screening cloud. We present the first large-scale numerical results on this controversial subject using exact diagonalization and density matrix renormalization group (RG). These extremely challenging numerical calculations confirm RG arguments for weak to strong coupling crossover with varying ring length and give results on the universal scaling functions. We also study, analytically and numerically, the important and surprising effects of particle-hole symmetry breaking.

cond-mat.str-el↗

arXiv2004

Susceptibility and Dzyaloshinskii-Moriya interaction in the Haldane gap compound NENP

The Haldane gap material NENP exhibits anomalies in its Knight shift, far infrared absorption and field-dependent gaps, which have been explained using the staggered $g$-tensor that occurs due to the low crystal symmetry. We point out that the low-temperature susceptibility is also anomalous and that a consistent interpretation of all data may require consideration of the Dzyaloshinskii-Moriya interaction.

cond-mat.str-el↗

arXiv2003

Non-Hermitian Luttinger Liquids and Vortex Physics

As a model of two thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar superconductor. When the applied field is tilted relative to the line defect, the physics is described by a nonhermitian Luttinger liquid of interacting quantum bosons in one spatial dimension with a point defect. We analyze this problem using a combination of analytic and numerical density matrix renormalization group methods, uncovering a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field. Interactions dramatically improve the ability of a single columnar pin to suppress vortex tilt when the Luttinger liquid parameter g is less than or equal to one.

cond-mat.mes-hall↗

arXiv2003

Kondo screening cloud effects in mesoscopic devices

We study how finite size effects may appear when a quantum dot in the Kondo Coulomb blockade regime is embedded into a mesoscopic device with finite wires. These finite size effects appear when the size of the mesoscopic device containing the quantum dot is of the order of the size of Kondo cloud and affect all thermodynamic and transport properties of the Kondo quantum dot. We also generalize our results to the experimentally relevant case where the wires contain several transverse modes/channels. Our results are based on perturbation theory, Fermi liquid theory and slave boson mean field theory.

cond-mat.mes-hall↗

arXiv2003

Junctions of three quantum wires and the dissipative Hofstadter model

We study a junction of three quantum wires enclosing a magnetic flux. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a non-trivial way. We present a direct connection between this problem and the dissipative Hofstadter problem, or quantum Brownian motion in two dimensions in a periodic potential and an external magnetic field, which in turn is connected to open string theory in a background electromagnetic field. We find non-trivial fixed points corresponding to a chiral conductance tensor leading to an asymmetric flow of the current.

cond-mat.str-el↗

arXiv2002

Reply to the "Comment on 'Neel order in doped quasi one-dimensional antiferromagnets'"

In a recent comment by A.A. Zvyagin to our Letter [Phys. Rev. Lett. 89, 47202 (2002)] it was pointed out that the bosonization treatment of the antiferromagnetic Heisenberg chain is only valid in the low temperature and long length limit. We support this statement and quantify the limits of validity by explicitly showing the crossover to the high temperature and/or short length limit using a combination of bosonization formulas and numerical results.

cond-mat.str-el↗

arXiv2002

Electron Spin Resonance in S=1/2 antiferromagnetic chains

A systematic field-theory approach to Electron Spin Resonance (ESR) in the $S=1/2$ quantum antiferromagnetic chain at low temperature $T$ (compared to the exchange coupling $J$) is developed. In particular, effects of a transverse staggered field $h$ and an exchange anisotropy (including a dipolar interaction) $δ$ on the ESR lineshape are discussed. In the lowest order of perturbation theory, the linewidth is given as $\propto Jh^2/T^2$ and $\propto (δ/J)^2 T$, respectively. In the case of a transverse staggered field, the perturbative expansion diverges at lower temperature; non-perturbative effects at very low temperature are discussed using exact results on the sine-Gordon field theory. We also compare our field-theory results with the predictions of Kubo-Tomita theory for the high-temperature regime, and discuss the crossover between the two regimes. It is argued that a naive application of the standard Kubo-Tomita theory to the Dzyaloshinskii-Moriya interaction gives an incorrect result. A rigorous and exact identity on the polarization dependence is derived for certain class of anisotropy, and compared with the field-theory results.

cond-mat.str-el↗

arXiv2002

Detecting the Kondo screening cloud in conductance measurements on quantum dots

The observation of the Kondo effect in quantum dots has provided new opportunities to finally observe the controversial Kondo screening cloud. We study how screening cloud effects appear in the conductance through a quantum wire containing a quantum dot when the length of the wire is comparable to the size of the screening cloud.

cond-mat.mes-hall↗

arXiv2002

Neel order in doped quasi one-dimensional antiferromagnets

We study the Neel temperature of quasi one-dimensional S=1/2 antiferromagnets containing non-magnetic impurities. We first consider the temperature dependence of the staggered susceptibility of finite chains with open boundary conditions, which shows an interesting difference for even and odd length chains. We then use a mean field theory treatment to incorporate the three dimensional inter-chain couplings. The resulting Neel temperature shows a pronounced drop as a function of doping by up to a factor of 5.

cond-mat.str-el↗

arXiv2001

The Kondo Screening Cloud

Renormalization group theory of the Kondo effect predicts that an impurity spin is screened by a conduction electron spread over a large distance of order >.1 to 1 micron. This review has the following sections: 1. The Kondo effect and the screening cloud, 2. Non-observation of the Kondo cloud in conventional experiments, 3. Kondo effect in transmission through a quantum dot, 4. Observing the screening cloud in persistent current experiments, 5. Side-coupled quantum dot, 6. Conclusions

cond-mat.str-el↗

arXiv2001

Friedel Oscillations and Charge Density Waves in Chains and Ladders

The density matrix renormalization group method for ladders works much more efficiently with open boundary conditions. One consequence of these boundary conditions is groundstate charge density oscillations that often appear to be nearly constant in magnitude or to decay only slightly away from the boundaries. We analyse these using bosonization techniques, relating their detailed form to the correlation exponent and distinguishing boundary induced generalized Friedel oscillations from true charge density waves. We also discuss a different approach to extracting the correlation exponent from the finite size spectrum which uses exclusively open boundary conditions and can therefore take advantage of data for much larger system sizes. A general discussion of the Friedel oscillation wave-vectors is given, and a convenient Fourier transform technique is used to determine it. DMRG results are analysed on Hubbard and t-J chains and 2 leg t-J ladders. We present evidence for the existence of a long-ranged charge density wave state in the t-J ladder at a filling of n=0.75 and near J/t \approx 0.25.

cond-mat.supr-con↗