We study the one-dimensional spin- $\frac{1}{2}$ Heisenberg model with antiferromagnetic nearest-neighbor ${J}_{1}$ and next-nearest-neighbor ${J}_{2}$ exchange couplings in magnetic field $h$ . With varying dimensionless parameters ${J}_{2}/{J}_{1}$ and $h/{J}_{1}$ , the ground state of the model exhibits several phases including three gapped phases (dimer, 1/3-magnetization plateau, and fully polarized phases) and four types of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2, spin-density-wave $({\text{SDW}}_{2})$ , and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various (multiple-)spin-correlation functions in detail and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1, ${\text{SDW}}_{2}$ , and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons (central charge $c=1+1$ ), which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-one-dimensional compounds are also discussed.We study the one-dimensional spin-$\frac{1}{2}$ Heisenberg model with antiferromagnetic nearest-neighbor ${J}_{1}$ and next-nearest-neighbor ${J}_{2}$ exchange couplings in magnetic field $h$. With varying dimensionless parameters ${J}_{2}/{J}_{1}$ and $h/{J}_{1}$, the ground state of the model exhibits several phases including three gapped phases (dimer, 1/3-magnetization plateau, and fully polarized phases) and four types of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2, spin-density-wave $({\text{SDW}}_{2})$, and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various (multiple-)spin-correlation functions in detail and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1, ${\text{SDW}}_{2}$, and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons (central charge $c=1+1$), which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-one-dimensional compounds are also discussed.

arXiv:1004.0622Physical Review BJun 28, 201063 citations

Fractionalized wave packets from an artificial Tomonaga–Luttinger liquid

大鎌田, Hiroshi Kamata, 倫雄熊田 +7 more

Feb 1, 20140 citations

Conductance of one-dimensional quantum wires

Ken‐Ichiro Imura, K.-V. Pham, Pascal Lederer +1 more

We discuss the conductance of quantum wires in terms of the Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge fractionalization scheme which results from the chiral symmetry of the model. We suggest that results of the standard two-terminal (2T) conductance measurement depend on the coupling of TLL with the reservoirs and can be interpreted as different boundary conditions at the interfaces. We propose a three-terminal (3T) geometry in which the third contact is connected weakly to the bulk of TLL subjected to a large bias current. We develop a renormalization-group (RG) analysis for this problem by taking explicitly into account the splitting of the injected electronic charge into two chiral irrational charges. We study in the presence of bulk contact the leading-order corrections to the conductance for two different boundary conditions, which reproduce in the absence of bulk contact, respectively, the standard 2T source-drain (SD) conductance ${G}_{\mathrm{SD}}^{(2)}{=e}^{2}/h$ and ${G}_{\mathrm{SD}}^{(2)}{=ge}^{2}/h,$ where g is the TLL charge interaction parameter. We find that under these two boundary conditions for the end contacts the 3T SD conductance ${G}_{\mathrm{SD}}^{(3)}$ shows an UV-relevant deviation from the above two values, suggesting new fixed points in the Ohmic limit. Nontrivial scaling exponents are predicted as a result of electron fractionalization.We discuss the conductance of quantum wires in terms of the Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge fractionalization scheme which results from the chiral symmetry of the model. We suggest that results of the standard two-terminal (2T) conductance measurement depend on the coupling of TLL with the reservoirs and can be interpreted as different boundary conditions at the interfaces. We propose a three-terminal (3T) geometry in which the third contact is connected weakly to the bulk of TLL subjected to a large bias current. We develop a renormalization-group (RG) analysis for this problem by taking explicitly into account the splitting of the injected electronic charge into two chiral irrational charges. We study in the presence of bulk contact the leading-order corrections to the conductance for two different boundary conditions, which reproduce in the absence of bulk contact, respectively, the standard 2T source-drain (SD) conductance ${G}_{\mathrm{SD}}^{(2)}{=e}^{2}/h$ and ${G}_{\mathrm{SD}}^{(2)}{=ge}^{2}/h,$ where g is the TLL charge interaction parameter. We find that under these two boundary conditions for the end contacts the 3T SD conductance ${G}_{\mathrm{SD}}^{(3)}$ shows an UV-relevant deviation from the above two values, suggesting new fixed points in the Ohmic limit. Nontrivial scaling exponents are predicted as a result of electron fractionalization.

arXiv:cond-mat/0111358Physical review. B, Condensed matterJul 11, 200237 citations

We study the one-dimensional spin-

\frac{1}{2}

Heisenberg model with antiferromagnetic nearest-neighbor

{J}_{1}

and next-nearest-neighbor

{J}_{2}

exchange couplings in magnetic field

h

. With varying dimensionless parameters

{J}_{2}/{J}_{1}

and

h/{J}_{1}

, the ground state of the model exhibits several phases including three gapped phases (dimer, 1/3-magnetization plateau, and fully polarized phases) and four types of gapless Tomonaga-Luttinger liquid (TLL) phases which we dub TLL1, TLL2, spin-density-wave

({\text{SDW}}_{2})

, and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various (multiple-)spin-correlation functions in detail and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1,

{\text{SDW}}_{2}

, and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons (central charge

c=1+1

), which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-one-dimensional compounds are also discussed.

{G}_{\mathrm{SD}}^{(2)}{=e}^{2}/h

and

{G}_{\mathrm{SD}}^{(2)}{=ge}^{2}/h,

where g is the TLL charge interaction parameter. We find that under these two boundary conditions for the end contacts the 3T SD conductance

{G}_{\mathrm{SD}}^{(3)}

shows an UV-relevant deviation from the above two values, suggesting new fixed points in the Ohmic limit. Nontrivial scaling exponents are predicted as a result of electron fractionalization.