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arXiv:1406.6149 · Physical Review B

Luttinger liquid behavior in the alternating spin-chain system copper nitrate

B. Willenberg, H. Ryll, Klaus H. Kiefer, D. M. Tennant, Felix Groitl, Katharina Rolfs, Pascal Manuel, Dmitry D. Khalyavin, K. C. Rule, Anja U. B. Wolter, Stefan Süllow

Published Feb 27, 2015• 24 citations
arXivHTMLPDF

Abstract

We determine the phase diagram of copper nitrate $\text{Cu}{({\text{NO}}_{3})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2.5{\mathrm{D}}_{2}\text{O}$ in the context of quantum phase transitions and novel states of matter. We establish this compound as an ideal candidate to study quasi-1D Luttinger liquids, 3D Bose-Einstein-Condensation of triplons, and the crossover between 1D and 3D physics. Magnetocaloric effect, magnetization, and neutron scattering data provide clear evidence for transitions into a Luttinger liquid regime and a 3D long-range ordered phase as a function of field and temperature. Theoretical simulations of this model material allow us to fully establish the phase diagram and to discuss it in the context of dimerized spin systems.

DOI
10.1103/physrevb.91.060407

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We determine the phase diagram of copper nitrate Cu(NO3)2\ifmmode⋅\else\textperiodcentered\fi2.5D2O\text{Cu}{({\text{NO}}_{3})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2.5{\mathrm{D}}_{2}\text{O}Cu(NO3​)2​\ifmmode⋅\else\textperiodcentered\fi2.5D2​O in the context of quantum phase transitions and novel states of matter. We establish this compound as an ideal candidate to study quasi-1D Luttinger liquids, 3D Bose-Einstein-Condensation of triplons, and the crossover between 1D and 3D physics. Magnetocaloric effect, magnetization, and neutron scattering data provide clear evidence for transitions into a Luttinger liquid regime and a 3D long-range ordered phase as a function of field and temperature. Theoretical simulations of this model material allow us to fully establish the phase diagram and to discuss it in the context of dimerized spin systems.
In the present work we aim to characterize the lattice configurations and the magnetic behavior in the incommensurate phase of spin-Peierls systems. This phase emerges when the magnetic exchange interaction is coupled to the distortions of an underlying triangular lattice and has its experimental realization in the quasi-one-dimensional compound family TiOXXX (X=ClX=\text{Cl}X=Cl, Br). With a simple model of spin-1/21/21/2 chains inserted in a planar triangular geometry which couples them elastically, we are able to obtain the uniform-incommensurate and incommensurate-dimerized phase transitions seen in these compounds. Moreover, we follow the evolution of the wave vector of the distortions with temperature inside the incommensurate phase. Finally, we predict gapless spin excitations for the intermediate phase of TiOXXX compounds along with incommensurate spin-spin correlations, offering to experimentalists a candidate to observe an exotic Luttinger liquidlike behavior.
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Distinct from the SU(2)\text{SU}(2)SU(2) case, the fermionic systems with SU(N)\text{SU}(N)SU(N) symmetry are expected to exhibit novel physics, such as exotic singlet formation. Using the density matrix renormalization group technique, we obtain the ground-state phase diagram of the SU(3)\text{SU}(3)SU(3) $t\text{\ensuremath{-}}J$ chain for density n<1n<1n<1. The ground-state phase diagram includes the Luttinger liquid, the extended Luther-Emery liquid characterized by a spin gap, and the phase separation state. We quantitatively assess the characteristics of the three phases by measuring spin gap, compressibility, various correlation functions, and structure factors. We further study the extended Luther-Emery liquid phase and discover molecular superfluid quasi-long-range order. The mechanism of the molecular superfluid is the combination of three SU(3)\text{SU}(3)SU(3) fermions on sites that are not entirely connected. Accordingly, we can speculate the behavior of the SU(N)\text{SU}(N)SU(N) $t\text{\ensuremath{-}}J$ chain model with larger NNN values, operating within the same filling regime.
We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.
Abstract We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 consisting of weakly coupled spin‐1/2 Heisenberg antiferromagnetic ladders. When placed in a magnetic field, such a ladder is theoretically predicted to exhibit a quantum critical Luttinger liquid (LL) behaviour in the gapless phase, i.e. between the two critical fields. Treating ladders as LLs and interaction between them as a perturbation, we are indeed able to fully account for (i) the spin dynamics accessed by measuring the spin–lattice relaxation rate T1−1T_1^{ - 1}T1−1​ , and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to the weak interladder coupling.
We calculate the correlation functions and the dc conductivity of Luttinger liquid superlattices, modelled by a repeated pattern of interacting and free Luttinger liquids. In a specific realization, where the interacting subsystem is a Hubbard chain, the system exhibits a rich phase diagram with four different phases: two metals and two compressible insulators. In general, we find that the effective low-energy description amalgamates features of both types of liquids in proportion to their spatial extent , suggesting the interesting possibility of `engineered' Luttinger liquids.