Wilson Ratio of a Tomonaga-Luttinger Liquid in a Spin-1/2Heisenberg Ladder

Honeycomb Heisenberg spin ladder: Unusual ground state and thermodynamic properties

“…Note that our result of R w = 3.98 on the conventional square ladder with J 1 , J 2 > 0 is consistent with that in Ref. [10]. These results show that the low-energy physics of both spin ladders are indeed distinct.…”

“…In magnetic fields, spin ladders could close the energy gaps and show the Tomonaga-Luttinger liquid (TLL) behavior with the linear temperature dependence of specific heat at low temperature. In recent years, the exotic properties of intriguing spin ladder materials like the S=1/2 two-leg compounds with AF legs (C 5 H 12 N) 2 CuBr 4 (BPCB) [6] and (C 7 H 10 N) 2 CuBr 4 (DIMPY) [7], with ferromagnetic (F) legs 3-Cl-4-F-V [3-(3-chloro-4-fluorophenyl)-1,5-diphenylverdazyl] [8], and with frustrations along the legs BiCu 2 PO 6 [9], etc., have been extensively explored, where novel quantum states and unconventional spinon excitations were disclosed [8,[10][11][12][13], illustrating that the spin ladders continue to surprise us in the area of strongly correlated quantum systems.…”

“…For the one-dimensional (1D) interacting electrons, the system demonstrates a Tomonaga-Luttinger liquid (TLL) behavior, and the Wilson ratio has the form of R w = 2/(1 + v s /v c ), which can be 1 in the noninteracting limit and approaches 2 in the strongly repulsive limit [28], where v s and v c are the velocities of spin and charge excitations. For 1D antiferromagnets including spin-1/2 and spin-1 linear AF chains as well as the two-leg square spin ladder in magnetic fields that also show the TLL behavior in gapless regimes, the Wilson ratio bears R w = 4K σ [10] with K σ the TLL parameter. By means of the LTRG method with D c =800, we calculated the Wilson ratio R w of the two-leg HC and square spin ladders at the lower critical magnetic field on which the gap corresponding to the m = 0 plateau closes, respectively, for a comparison.…”

Giant magnetic field dependence of the coupling between spin chains inBaCo2V2O8

“…The simplest and experimentally most accessible TLLs are realized in 1D quantum antiferromagnets hosting spin chains or ladders, which can be mapped onto interacting spinless fermions [8]. In particular, two spin-ladder systems, (C 5 H 12 N) 2 CuBr 4 (BPCB) [9-13] and (C 7 H 10 N) 2 CuBr 4 (DIMPY) [14][15][16][17][18][19], allowed to confirm the predicted correlation functions not only in form, but also quantitatively as a function of the magnetic field, which controls the Fermi level [1].While isolated TLLs cannot order because of strong quantum fluctuations, a weak coupling between TLLs leads at low temperatures to the 3D ordered state, which inherits the properties of the dominant fluctuation mode.As the Fermi surface in a TLL is reduced to two points, k F and −k F , fermionic fluctuations can only occur at the wavevectors q = 0 and q = 2k F [1]. In antiferromagnetic spin chains or ladders in a magnetic field, the corresponding spin fluctuations are transverse (i.e., involving spin components perpendicular to the field) antiferromagnetic, at the antiferromagnetically shifted wavevector q = π, and longitudinal (i.e., involving spin components along the field) incommensurate at the incommensurate wavevector q = 2k F , respectively [1].…”

“…The simplest and experimentally most accessible TLLs are realized in 1D quantum antiferromagnets hosting spin chains or ladders, which can be mapped onto interacting spinless fermions [8]. In particular, two spin-ladder systems, (C 5 H 12 N) 2 CuBr 4 (BPCB) [9][10][11][12][13] and (C 7 H 10 N) 2 CuBr 4 (DIMPY) [14][15][16][17][18][19], allowed to confirm the predicted correlation functions not only in form, but also quantitatively as a function of the magnetic field, which controls the Fermi level [1].…”