The von Neumann entanglement entropy is studied with the density-matrix renormalization-group technique. We propose a simple approach to calculate the central charge using the entanglement entropy for a one-dimensional (1D) quantum system. This approach is applied to a couple of quantum systems: (i) a 1D frustrated spin model and (ii) a 1D half-filled spinless fermions with nearest-neighbor repulsion; it is confirmed that the central charge is estimated very accurately for the both systems. Also, a new method to determine the critical point between Tomonaga-Luttinger-liquid and gapped (or ordered) phases from the proposed approach is suggested. Furthermore, we mention that the Tomonaga-Luttinger parameter can be obtained in a like manner as the central charge, using the charge-density fluctuation of a part of the 1D system.The von Neumann entanglement entropy is studied with the density-matrix renormalization-group technique. We propose a simple approach to calculate the central charge using the entanglement entropy for a one-dimensional (1D) quantum system. This approach is applied to a couple of quantum systems: (i) a 1D frustrated spin model and (ii) a 1D half-filled spinless fermions with nearest-neighbor repulsion; it is confirmed that the central charge is estimated very accurately for the both systems. Also, a new method to determine the critical point between Tomonaga-Luttinger-liquid and gapped (or ordered) phases from the proposed approach is suggested. Furthermore, we mention that the Tomonaga-Luttinger parameter can be obtained in a like manner as the central charge, using the charge-density fluctuation of a part of the 1D system.

arXiv:1110.4340Physical Review BNov 4, 201156 citations

DENSITY-MATRIX RENORMALIZATION GROUP METHOD FOR TOMONAGA-LUTTINGER LIQUID

TOSHIYA HIKIHARA

Jul 16, 20120 citations

The Conductivity of the Tomonaga‐Luttinger Model

Victor Bârsan

physica status solidi (b)Jun 1, 19890 citations

Tunneling density of states in a Y junction of Tomonaga-Luttinger liquid wires: A density matrix renormalization group study

Monalisa Singh Roy, Manoranjan Kumar, Sourin Das

It is well known that the pristine bulk of an interacting one-dimensional system in Tomonaga-Luttinger liquid (TLL) phase shows power law suppression of quasiparticle tunneling amplitude for all values of TLL parameter $g$ , in the zero-energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting bosons case and (b) interacting fermions case, when $g>1$ . We also observe suppression of TDOS for $g<1$ for both bosonic and fermionic cases. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points, owing to statistical correlations that play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fixed point for $1<g<3$ resembles the mysterious $M$ fixed point of Y junction predicted by Oshikawa, Chamon, and Affleck [J. Stat. Mech. (2006) P02008]. We also show that the TDOS enhancement spans over a length scale of $\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1}$ from the junction, for $1<g<3$ .It is well known that the pristine bulk of an interacting one-dimensional system in Tomonaga-Luttinger liquid (TLL) phase shows power law suppression of quasiparticle tunneling amplitude for all values of TLL parameter $g$, in the zero-energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting bosons case and (b) interacting fermions case, when $g>1$. We also observe suppression of TDOS for $g<1$ for both bosonic and fermionic cases. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points, owing to statistical correlations that play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fixed point for $1<g<3$ resembles the mysterious $M$ fixed point of Y junction predicted by Oshikawa, Chamon, and Affleck [J. Stat. Mech. (2006) P02008]. We also show that the TDOS enhancement spans over a length scale of $\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1}$ from the junction, for $1<g<3$.

arXiv:1912.13040Physical review. B./Physical review. BJul 17, 20203 citations

Scaling of temporal correlations in an attractive Tomonaga-Luttinger spin liquid

Kirill Yu. Povarov, D. Schmidiger, N. Reynolds +2 more

We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder ${({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}$ in a magnetic field $H=9$ T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter $K\ensuremath{\approx}1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder ${({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}$ in a magnetic field $H=9$ T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter $K\ensuremath{\approx}1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.

arXiv:1406.6876Physical Review BJan 23, 201534 citations

Luttinger Revisited—The Renormalization Group Approach

R. Shankar

Journal of Statistical PhysicsMay 1, 20013 citations

g

, in the zero-energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting bosons case and (b) interacting fermions case, when

g>1

. We also observe suppression of TDOS for

g<1

for both bosonic and fermionic cases. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points, owing to statistical correlations that play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fixed point for

1<g<3

resembles the mysterious

M

fixed point of Y junction predicted by Oshikawa, Chamon, and Affleck [J. Stat. Mech. (2006) P02008]. We also show that the TDOS enhancement spans over a length scale of $\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1}$ from the junction, for

1<g<3

We report temperature-dependent neutron scattering measurements of the local dynamic structure factor in the quantum spin ladder

{({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}

in a magnetic field

H=9

T, in its gapless quantum-critical phase. We show that the measured quantity has a scaling form consistent with expectations for a Tomonaga-Luttinger liquid with attraction. The measured Luttinger parameter $K\ensuremath{\approx}1.25$ and scaling function are in excellent agreement with density matrix renormalization group numerical calculations for the underlying spin Hamiltonian.