arXiv subjects

Diptiman Sen

Publications and source records attributed to Diptiman Sen.

At least 145 records · Page 8Linked to original sources

arXiv2007

Low energy properties of the SU(m|n) supersymmetric Haldane-Shastry spin chain

The ground state and low energy excitations of the SU(m|n) supersymmetric Haldane-Shastry spin chain are analyzed. In the thermodynamic limit, it is found that the ground state degeneracy is finite only for the SU(m|0) and SU(m|1) spin chains, while the dispersion relation for the low energy and low momentum excitations is linear for all values of m and n. We show that the low energy excitations of the SU(m|1) spin chain are described by a conformal field theory of m non-interacting Dirac fermions which have only positive energies; the central charge of this theory is m/2. Finally, for n \ge 1, the partition functions of the SU(m|n) Haldane-Shastry spin chain and the SU(m|n) Polychronakos spin chain are shown to be related in a simple way in the thermodynamic limit at low temperatures.

hep-th↗

arXiv2007

Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain

By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation.

hep-th↗

arXiv2007

Charge transport in a Tomonaga-Luttinger liquid: effects of pumping and bias

We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, point-like impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K - 1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current becomes large for special values of the bias. For non-interacting electrons with K = 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.

cond-mat.mes-hall↗

arXiv2007

Correlators and fractional statistics in the quantum Hall bulk

We derive single-particle and two-particle correlators of anyons in the presence of a magnetic field in the lowest Landau level. We show that the two-particle correlator exhibits signatures of fractional statistics which can distinguish anyons from their fermionic and bosonic counterparts. These signatures include the zeroes of the two-particle correlator and its exclusion behavior. We find that the single-particle correlator in finite geometries carries valuable information relevant to experiments in which quasiparticles on the edge of a quantum Hall system tunnel through its bulk.

cond-mat.mes-hall↗

arXiv2007

Spin-1 chain with spin-1/2 excitations in the bulk

We present a spin-1 chain with a Hamiltonian which has three exactly solvable ground states. Two of these are fully dimerized, analogous to the Majumdar-Ghosh (MG) states of a spin-1/2 chain, while the third is of the Affleck-Kennedy-Lieb-Tasaki (AKLT) type. We use variational and numerical methods to study the low-energy excitations which interpolate between these ground states in different ways. In particular, there is a spin-1/2 excitation which interpolates between the MG and AKLT ground states; this is the lowest excitation of the system and it has a surprisingly small gap. We discuss generalizations of our model of spin fractionalization to higher spin chains and higher dimensions.

cond-mat.str-el↗

arXiv2007

DMRG study of scaling exponents in spin-1/2 Heisenberg chains with dimerization and frustration

In conformal field theory, key properties of spin-1/2 chains, such as the ground state energy per site and the excitation gap scale with dimerization delta as delta^alpha with known exponents alpha and logarithmic corrections. The logarithmic corrections vanish in a spin chain with nearest (J=1) and next nearest neighbor interactions (J_2), for J_2c=0.2411. DMRG analysis of a frustrated spin chain with no logarithmic corrections yields the field theoretic values of alpha, and the scaling relation is valid up to the physically realized range, delta ~ 0.1. However, chains with logarithmic corrections (J_2<0.2411 J) are more accurately fit by simple power laws with different exponents for physically realized dimerizations. We show the exponents decreasing from approximately 3/4 to 2/3 for the spin gap and from approximately 3/2 to 4/3 for the energy per site and error bars in the exponent also decrease as J_2 approaches to J_2c.

cond-mat.str-el↗

arXiv2007

Equation of motion approach to non-adiabatic quantum charge pumping

We use the equations of motion of non-interacting electrons in a one-dimensional system to numerically study different aspects of charge pumping. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the Fourier transforms of the charge and energy currents in the leads. Our method works for all values of parameters, and gives the complete time-dependences of the current and charge at any site of the system. Our results agree with Floquet and adiabatic scattering theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a traveling potential wave. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias.

cond-mat.mes-hall↗

arXiv2006

Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point

We study an infinite range ferromagnetic Ising model in the presence of a transverse magnetic field which exhibits a quantum paramagnetic-ferromagnetic phase transition at a critical value of the transverse field. In the thermodynamic limit, the low-temperature properties of this model are dominated by the behavior of a single large classical spin governed by an anisotropic Hamiltonian. Using this property, we study the quench and AC dynamics of the model both numerically and analytically, and develop a correspondence between the classical phase space dynamics of a single spin and the quantum dynamics of the infinite-range ferromagnetic Ising model. In particular, we compare the behavior of the equal-time order parameter correlation function both near to and away from the quantum critical point in the presence of a quench or AC transverse field. We explicitly demonstrate that a clear signature of the quantum critical point can be obtained by studying the AC dynamics of the system even in the classical limit. We discuss possible realizations of our model in experimental systems.

cond-mat.stat-mech↗

arXiv2006

Gapless points of dimerized quantum spin chains: analytical and numerical studies

We study the locations of the gapless points which occur for quantum spin chains of finite length (with a twisted boundary condition) at particular values of the nearest neighbor dimerization, as a function of the spin S and the number of sites. For strong dimerization and large values of S, a tunneling calculation reproduces the same results as those obtained from more involved field theoretic methods using the non-linear sigma-model approach. A different analytical calculation of the matrix element between the two Neel states gives a set of gapless points; for strong dimerization, these differ significantly from the tunneling values. Finally, the exact diagonalization method for a finite number of sites yields a set of gapless points which are in good agreement with the Neel state calculations for all values of the dimerization, but the agreement with the tunneling values is not very good even for large S. This raises questions about possible corrections to the tunneling results.

cond-mat.str-el↗

arXiv2006

Renormalization group study of the Kondo problem at a junction of several Luttinger wires

We study a system consisting of a junction of N quantum wires, where the junction is characterized by a scalar S-matrix, and an impurity spin is coupled to the electrons close to the junction. The wires are modeled as weakly interacting Tomonaga-Luttinger liquids. We derive the renormalization group equations for the Kondo couplings of the spin to the electronic modes on different wires, and analyze the renormalization group flows and fixed points for different values of the initial Kondo couplings and of the junction S-matrix (such as the decoupled S-matrix and the Griffiths S-matrix). We generally find that the Kondo couplings flow towards large and antiferromagnetic values in one of two possible ways. For the Griffiths S-matrix, we study one of the strong coupling flows by a perturbative expansion in the inverse of the Kondo coupling; we find that at large distances, the system approaches the ferromagnetic fixed point of the decoupled S-matrix. For the decoupled S-matrix with antiferromagnetic Kondo couplings and weak inter-electron interactions, the flows are to one of two strong coupling fixed points in which all the channels are strongly coupled to each other through the impurity spin. But strong inter-electron interactions, with K_ρ< N/(N+2), stabilize a multi-channel fixed point in which the coupling between different channels goes to zero. We have also studied the temperature dependence of the conductance at the decoupled and Griffiths S-matrices.

cond-mat.str-el↗

arXiv2006

A multi-channel fixed point for a Kondo spin coupled to a junction of Luttinger liquids

We study a system of an impurity spin coupled to a junction of several Tomonaga-Luttinger liquids using a renormalization group scheme. For the decoupled S-matrix at the junction, there is a range of Kondo couplings which flow to a multi-channel fixed point for repulsive inter-electron interactions; this is associated with a characteristic temperature dependence of the spin-flip scatterings. If the junction is governed by the Griffiths S-matrix, the Kondo couplings flow to a strong coupling fixed point where all the wires are decoupled.

cond-mat.str-el↗

arXiv2006

Conductance of quantum wires: a numerical study of the effects of an impurity and interactions

We use the non-equilibrium Green's function formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire. We study how the conductance varies with the wire length, the temperature, and the strength of the impurity and interactions. The dependence of the conductance on the wire length and temperature is found to be in rough agreement with the results obtained from a renormalization group analysis based on the Hartree-Fock approximation. For the spin-1/2 model with a repulsive on-site interaction or the spinless model with an attractive nearest neighbor interaction, we find that the conductance increases with increasing wire length or decreasing temperature. This can be qualitatively explained using the Born approximation in scattering theory. For a strong impurity, the conductance is significantly different for a repulsive and an attractive impurity; this is due to the existence of a bound state in the latter case. In general, the large density deviations at short distances have an appreciable effect on the conductance which is not captured by the renormalization group analysis.

cond-mat.str-el↗

arXiv2006

Non-equilibrium Green's function formalism and the problem of bound states

The non-equilibrium Green's function formalism for infinitely extended reservoirs coupled to a finite system can be derived by solving the equations of motion for a tight-binding Hamiltonian. While this approach gives the correct density for the continuum states, we find that it does not lead, in the absence of any additional mechanisms for equilibration, to a unique expression for the density matrix of any bound states which may be present. Introducing some auxiliary reservoirs which are very weakly coupled to the system leads to a density matrix which is unique in the equilibrium situation, but which depends on the details of the auxiliary reservoirs in the non-equilibrium case.

cond-mat.mes-hall↗

arXiv2005

Inter-edge interactions and novel fixed points at a junction of quantum Hall line junctions

We show that novel fixed points (characterized by matrices which specify the splitting of the currents at the junction) can be accessed in a system which contains a junction of three quantum Hall line junctions. For such a junction of fractional quantum Hall edge states, we find that it is possible for both the flower (single droplet) and islands (three droplets) configurations to be stable in an intermediate region, for a range of values of the inter-edge repulsive interactions. A measurement of the tunneling conductance as a function of the gate voltage controlling inter-edge repulsions can give a clear experimental signal of this region.

cond-mat.mes-hall↗

arXiv2005

Multi-band structure of the quantum bound states for a generalized nonlinear Schrodinger model

By using the method of coordinate Bethe ansatz, we study N-body bound states of a generalized nonlinear Schrodinger model having two real coupling constants c and η. It is found that such bound states exist for all possible values of c and within several nonoverlapping ranges (called bands) of η. The ranges of ηwithin each band can be determined completely using Farey sequences in number theory. We observe that N-body bound states appearing within each band can have both positive and negative values of the momentum and binding energy.

hep-th↗

arXiv2004

Quantum bound states for a derivative nonlinear Schrodinger model and number theory

A derivative nonlinear Schrodinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant eta. The ranges of eta within each band can be completely determined using number theoretic concepts such as Farey sequences and continued fractions. For N > 2, the N-body bound states can have both positive and negative momentum. For eta > 0, bound states with positive momentum have positive binding energy, while states with negative momentum have negative binding energy.

hep-th↗

arXiv2004

Tunneling through two resonant levels: fixed points and conductances

We study point contact tunneling between two leads of a Tomonaga-Luttinger liquid through two degenerate resonant levels in parallel. This is one of the simplest cases of a quantum junction problem where the Fermi statistics of the electrons plays a non-trivial role through the Klein factors appearing in bosonization. Using a mapping to a `generalized Coulomb model' studied in the context of the dissipative Hofstadter model, we find that any asymmetry in the tunneling amplitudes from the two leads grows at low temperatures, so that ultimately there is no conductance across the system. For the symmetric case, we identify a non-trivial fixed point of this model; the conductance at that point is generally different from the conductance through a single resonant level.

cond-mat.mes-hall↗

arXiv2004

Magnetic properties of a helical spin chain with alternating isotropic and anisotropic spins: magnetization plateaus and finite entropy

We study a model which could explain some of the unusual magnetic properties observed for the one-dimensional helical spin system Co(hfac)_2 NITPhOMe. One of the properties observed is that the magnetization shows plateaus near zero and near one-third of the saturation value if a magnetic field is applied along the helical axis, but not if the field is applied in the plane perpendicular to that axis. The system consists of a spin-1/2 chain in which cobalt ions (which are highly anisotropic with an easy axis e_i) and organic radicals (which are isotropic) alternate with each other. The easy axis of the cobalts e_i lie at an angle theta_i with respect to the helical axis, while the projection of e_{i+1} - e_i on the plane perpendicular to the helical axis is given by 2 pi /3. For temperatures and magnetic fields which are much smaller than the coupling between the nearest-neighbor cobalts and radicals, one can integrate out the radicals to obtain an Ising model for the cobalts; this enables one to compute the thermodynamic properties of the system using the transfer matrix approach. We consider a model in which the tilt angles theta_i are allowed to vary with i with period three; we find that for certain patterns of theta_i, the system shows the magnetization plateaus mentioned above. At the ends of the plateaus, the entropy is finite even at very low temperatures, while the magnetic susceptibility and specific heat also show some interesting features.

cond-mat.stat-mech↗