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P. Lecheminant

Publications and source records attributed to P. Lecheminant.

50 records · Page 3Linked to original sources
arXiv2001

Phase transitions in the one-dimensional spin-S $J_1-J_2$ XY model

The one-dimensional spin-S $J_1-J_2$ XY model is studied within the bosonization approach. Around the two limits ($J_2/J_1 \ll 1,J_2/J_1 \gg 1$) where a field theoretical analysis can be derived, we discuss the phases as well as the different phase transitions that occur in the model. In particular, it is found that the chiral critical spin nematic phase, first discovered by Nersesyan et al. (Phys. Rev. Lett. {\bf 81}, 910 (1998)) for $S=1/2$, exists in the general spin-S case. The nature of the effective field theory that describes the transition between this chiral critical phase and a chiral gapped phase is also determined.

cond-mat.str-el↗
arXiv2000

Spontaneous plaquette formation in the SU(4) Spin-Orbital ladder

The low-energy properties of the SU(4) spin-orbital model on a two-leg ladder are studied by a variety of analytical and numerical techniques. Like in the case of SU(2) models, there is a singlet-multiplet gap in the spectrum, but the ground-state is two-fold degenerate. An interpretation in terms of SU(4)-singlet plaquettes is proposed. The implications for general two-dimensional lattices are outlined.

cond-mat.str-el↗
arXiv2000

Composite Pairings in Chirally Stabilized Critical Fluids

We study a one-dimensional electron gas in a special antiferromagnetic environment made by two spin-1/2 Heisenberg chains and the 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.

cond-mat.str-el↗
arXiv1999

Chirally Stabilized Critical State in Marginally Coupled Spin and Doped Systems

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.

cond-mat.str-el↗
arXiv1999

Theory Of The One Dimensional SU(4) Spin-Orbital Model

The one-dimensional spin-orbital model is studied by means of Abelian bosonization. We derive the low-energy effective theory which enables us to study small deviations from the SU(4) symmetric point. We show that there exists a massless region with algebraically decaying correlation functions, $\sim \cos(π/{2a_0} x) x^{-3/2}$. When entering the massive phase, the system displays an approximate SO(6) enlarged symmetry with a dimerization type of ordering consisting in alternating spin and orbital singlets.

cond-mat.str-el↗
arXiv1998

Kagom{é} Lattice Antiferromagnet Stripped to Its Basics

We study a model of a spin S = 1/2 Heisenberg antiferromagnet on a one dimensional lattice with the local symmetry of the two dimensional kagom{é} lattice. Using three complementary approaches, it is shown that the low energy spectrum can be described by two critical Ising models with different velocities. One of these velocities is small, leading to a strongly localized Majorana fermion. These excitations are singlet ones whereas the triplet sector has a spectral gap.

cond-mat.str-el↗
arXiv1998

New Chiral Universality Class in a Frustrated Three-Leg Spin Ladder

We study a model of three $S=1/2$ 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=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 the new 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. We discuss the spectral properties of the model, compute spin-spin correlation functions and estimate the NMR relaxation rate.

cond-mat.str-el↗
arXiv1998

The Wilson Renormalization Group Approach of the Principal Chiral Model around Two Dimensions

We study the Principal Chiral Ginzburg-Landau-Wilson model around two dimensions within the Local Potential Approximation of an Exact Renormalization Group equation. This model, relevant for the long distance physics of classical frustrated spin systems, exhibits a fixed point of the same universality class that the corresponding Non-Linear Sigma model. This allows to shed light on the long-standing discrepancy between the different perturbative approaches of frustrated spin systems.

hep-th↗
arXiv1998

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic ($ΔS=1$) excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic ($ΔS=0$) excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets.

cond-mat.stat-mech↗
arXiv1997

Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{é} lattice: an approach through exact spectra analysis

A group symmetry analysis of the low lying levels of the spin-1/2 kagomé Heisenberg antiferromagnet is performed for small samples up to N=27. This approach allows to follow the effect of quantum fluctuations when the sample size increases. The results contradict the scenario of ``order by disorder'' which has been advanced on the basis of large S calculations. A large enough second neighbor ferromagnetic exchange coupling is needed to stabilize the $\sqrt 3 \times \sqrt 3$ pattern: the finite size analysis indicates a quantum critical transition at a non zero coupling.

cond-mat.str-el↗
arXiv1995

The massive $CP^{N-1}$ model for frustrated spin systems

We study the classical ${SU(N)\otimes U(1)/SU(N-1)\otimes U(1)}$ Non Linear Sigma model which is the continuous low energy effective field theory for $N$ component frustrated spin systems. The $β$ functions for the two coupling constants of this model are calculated around two dimensions at two loop order in a low temperature expansion. Our study is completed by a large $N$ analysis of the model. The $β$ functions for the coupling constants and the mass gap are calculated in all dimensions between 2 and 4 at order ${1/N}$. As a main result we show that the standard procedure at the basis of the $1/N$ expansion leads to results that partially contradict those of the weak coupling analysis. We finally present the procedure that reconciles the weak coupling and large $N$ analysis, giving a consistent picture of the expected scaling of frustrated magnets.

cond-mat↗
arXiv1995

$J_1-J_2$ quantum Heisenberg antiferromagnet on the triangular lattice: a group symmetry analysis of order by disorder

On the triangular lattice, for $J_2/J_1$ between $1/8$ and $1$, the classical Heisenberg model with first and second neighbor interactions presents four-sublattice ordered ground-states. Spin-wave calculations of Chubukov and Jolicoeur\cite{cj92} and Korshunov\cite{k93} suggest that quantum fluctuations select amongst these states a colinear two-sublattice order. From theoretical requirements, we develop the full symmetry analysis of the low lying levels of the spin-1/2 Hamiltonian in the hypotheses of either a four or a two-sublattice order. We show on the exact spectra of periodic samples ($N=12,16$ and $28$) how quantum fluctuations select the colinear order from the four-sublattice order.

cond-mat↗
arXiv1994

Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice

Exact spectra of periodic samples are computed up to $ N=36 $. Evidence of an extensive set of low lying levels, lower than the softest magnons, is exhibited. These low lying quantum states are degenerated in the thermodynamic limit; their symmetries and dynamics as well as their finite-size scaling are strong arguments in favor of Néel order. It is shown that the Néel order parameter agrees with first-order spin-wave calculations. A simple explanation of the low energy dynamics is given as well as the numerical determinations of the energies, order parameter and spin susceptibilities of the studied samples. It is shown how suitable boundary conditions, which do not frustrate Néel order, allow the study of samples with $ N=3p+1 $ spins. A thorough study of these situations is done in parallel with the more conventional case $ N=3p $.

cond-mat↗