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Chirally Stabilized Critical State in Marginally Coupled Spin Systems

P. Azaria, P. Lecheminant

Published Dec 22, 1999• 0 citations
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Abstract

We study a class of one-dimensional models consisting of a frustrated (N+1)-leg spin ladder, its asymmetric doped version as a special example of a Luttinger liquid in an active environment, and the N-channel Kondo-Heisenberg model away from half-filling. It is shown that these models exhibit a critical phase with generally a non-integer central charge and belong to the class of chirally stabilized spin liquids recently introduced by Andrei, Douglas, and Jerez [Phys. Rev. B 58, 7619 (1998)]. By allowing anisotropic interactions in spin space, an exact solution in the N=2 case is found at a Toulouse point which captures all universal properties of the models. At the critical point, the massless degrees of freedom are described in terms of an effective S=1/2 Heisenberg spin chain and two critical Ising models. The Toulouse limit solution enables us to discuss the spectral properties, the computation of the spin-spin correlation functions as well as the estimation of the NMR relaxation rate of the frustrated three-leg ladder. Finally, it is shown that the critical point becomes unstable upon switching on some weak backscattering perturbations in the frustrated three-leg ladder.

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We study a class of one-dimensional models consisting of a frustrated (N+1)-leg spin ladder, its asymmetric doped version as a special example of a Luttinger liquid in an active environment, and the N-channel Kondo-Heisenberg model away from half-filling. It is shown that these models exhibit a critical phase with generally a non-integer central charge and belong to the class of chirally stabilized spin liquids recently introduced by Andrei, Douglas, and Jerez [Phys. Rev. B 58, 7619 (1998)]. By allowing anisotropic interactions in spin space, an exact solution in the N=2 case is found at a Toulouse point which captures all universal properties of the models. At the critical point, the massless degrees of freedom are described in terms of an effective S=1/2 Heisenberg spin chain and two critical Ising models. The Toulouse limit solution enables us to discuss the spectral properties, the computation of the spin-spin correlation functions as well as the estimation of the NMR relaxation rate of the frustrated three-leg ladder. Finally, it is shown that the critical point becomes unstable upon switching on some weak backscattering perturbations in the frustrated three-leg ladder.
We study a model of three S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg spin chains weakly coupled by on-rung and plaquette-diagonal interchain interactions. It is shown that the model exhibits a critical phase with central charge C=2C=2C=2 and belongs to the class of ``chirally stabilized'' liquids recently introduced by Andrei, Douglas, and Jerez. By allowing anisotropic interactions in spin space, we find an exact solution at a Toulouse point which captures all universal properties of the model, including the SU(2) symmetric case. At this critical point the massless degrees of freedom are described in terms of an effective S=1/2S=1/2S=1/2 Heisenberg spin chain and two critical Ising models. We discuss the spectral properties of the model, compute spin-spin correlation functions, and estimate the NMR relaxation rate.
We study a one-dimensional electron gas in a special antiferromagnetic environment made by two spin-1/2 Heisenberg chains and a one-dimensional two-channel Kondo-Heisenberg lattice away from half-filling. These models flow to an intermediate fixed point which belongs to the universality class of chirally stabilized liquids. Using a Toulouse point approach, the universal properties of the models are determined as well as the identification of the leading instabilities. It is shown that these models exhibit a non-Fermi-liquid behavior with strong enhanced composite pairing correlations.
We investigate the ground-state phase diagram of a frustrated spin-1/2 Heisenberg ladder in the transverse magnetic field with an anisotropic inter-rung exchange coupling ααα. This bond-anisotropic parameter continuously interpolates among the Ising-like limit α=0α=0α=0, the isotropic point α=1α=1α=1, and the XY-dominated regime α≫1α\gg 1α≫1. Using density-matrix renormalization group calculations within a matrix-product-state framework, we analyze bipartite entanglement, magnetization, and spin correlations to characterize the emergent quantum phases. We identify six distinct ground-state phases, including rung-singlet, Haldane-like, Tomonaga-Luttinger liquid, canted Ising-ordered, XY-polarized, and ordered ferromagnetic states. While magnetization and local correlations provide a first insight into phase classifications, the finite-size scaling of the entanglement measures offers a more sensitive and unified diagnostics of both gapped and gapless regimes. In the gapless regime, we extract the central charge c≃1c \simeq 1c≃1, confirming Tomonaga-Luttinger liquid behavior, while at the transition between the canted Ising and ferromagnetic phases, we observe c≃1/2c \simeq 1/2c≃1/2, consistent with the Ising universality. Finally, we find that both the Haldane-like behavior and the extended critical Tomonaga-Luttinger liquid regime are strongly confined to the vicinity of the isotropic point α=1α= 1α=1.
Using the density matrix renormalization group method we have studied the ground-state phase diagram of a spin-1/2 frustrated three-leg antiferromagnetic Heisenberg ladder, and identified two phases corresponding to the spin-3/2 chain and the standard spin ladder. Varying the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ leads to a quantum phase transition from one ground state to the other, but does not alter the gapless nature of the excitation spectra. On the phase boundary, the degenerate ground states form a chiral spin liquid with a central charge c=2.c=2.c=2. The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.
We study a lattice realization of a Luttinger liquid interacting with quantum spins in terms of an antiferromagnetic S=1∕2S=1∕2S=1∕2 Heisenberg chain, where each spin is also coupled to a $\ensuremath{\sigma}=1∕2$ Kondo spin degree of freedom. This model describes the low-energy spin dynamics in quasi-one-dimensional materials, where the electronic spins of the magnetic ions interact with those of impurities, nuclei, and possibly other spin species present in their environment. For large ferromagnetic and antiferromagnetic Kondo interaction ${J}^{\ensuremath{'}}$, there are two phases corresponding to an effective spin-1 Heisenberg chain and a dimerized spin-1∕21∕21∕2 ladder, respectively. For weak Kondo interaction, we establish that the Kondo interaction drives the system to a strong coupling regime. This suggests that ${J}^{\ensuremath{'}}=0$ is the only critical point in the system.
Using a recently proposed perturbative numerical renormalization-group algorithm, we explore the connection between quantum criticality and the emergence of Luttinger liquid physics in t−Jt-Jt−J chains coupled by frustrated interactions. This study is built on an earlier finding that at the maximally frustrated point, the ground state of weakly-coupled Heisenberg chains is disordered, the transverse exchanges being irrelevant. This result is extended here to transverse couplings up to J⊥=0.6J_{\perp}=0.6J⊥​=0.6, and we argue that it may also be valid at the isotropic point. A finite size analysis of coupled Heisenberg chains in the vicinity of the maximally frustrated point confirms that the transverse spin-spin correlations decay exponentially while the longitudinal ones revert to those of decoupled chains. We find that this behavior persists upon moderate hole doping $x \alt 0.75$. For larger doping, the frustration becomes inactive and the quantum critical point is suppressed.