Decoherence induced by an ordered environment

This Letter deals with the time evolution of a qubit weakly coupled to a reservoir which has a symmetry broken state with long range order at finite temperatures. In particular, we model the ordered reservoir by a standard BCS superconductor with s-wave pairing. We study the reduced density matrix of a qubit using both the time-convolutionless and Nakajima-Zwanzig approximations. We study different kinds of couplings between the qubit and the superconducting bath. We find that ordering in the superconducting bath generically leads to an unfavorable non- Markovian faster-than-exponential decay of the qubit coherence. On the other hand, a coupling of the qubit to the non-ordered sector of the bath can result in a Markovian decoherence of the qubit with a drastic reduction of the decoherence rate. Since these behaviors are endemic to the ordered phase, qubits can serve as useful probes of continuous phase transitions in their environment. We also briefly discuss the validity of our main result, faster than exponential decay of the qubit coherences, for a qubit coupled to a generic ordered bath with a spontaneously broken continuous symmetry at finite temperatures.Comment: 6 pages, 3 figure

Spectrum of elementary and collective excitations in the dimerized S=1/2 Heisenberg chain with frustration

We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter $\delta$ is not too small ($\delta>0.1$), i.e. while the elementary triplets can be treated as localized objects.Comment: 18 pages, 13 figure

Three-Dimensional Ordering in Weakly Coupled Antiferromagnetic Ladders and Chains

A theoretical description is presented for low-temperature magnetic-field induced three-dimensional (3D) ordering transitions in strongly anisotropic quantum antiferromagnets, consisting of weakly coupled antiferromagnetic spin-1/2 chains and ladders. First, effective continuum field theories are derived for the one-dimensional subsystems. Then the Luttinger parameters, which determine the low-temperature susceptibilities of the chains and ladders, are calculated from the Bethe ansatz solution for these effective models. The 3D ordering transition line is obtained using a random phase approximation for the weak inter-chain (inter-ladder) coupling. Finally, considering a Ginzburg criterion, the fluctuation corrections to this approach are shown to be small. The nature of the 3D ordered phase resembles a Bose condensate of integer-spin magnons. It is proposed that for systems with higher spin degrees of freedom, e.g. N-leg spin-1/2 ladders, multi-component condensates can occur at high magnetic fields.Comment: RevTex, 18 pages with 7 figure

Spin-density Wave in Ising-coupled Antiferromagnetic Chains

The effect of anisotropy in the nearest-neighbor spin interactions that couple $N\geq 2$ consecutive spin-1/2 antiferromagnetic chains is studied theoretically by considering the limit where the coupling is purely of the Ising type. An analysis based on the equivalent Luttinger model reveals that the groundstate is an Ising antiferromagnet in general.Comment: 11 pgs. of plain TeX, one postscript fig., to appear in Phys. Rev.

Disordered periodic systems at the upper critical dimension

The effects of weak point-like disorder on periodic systems at their upper critical dimension D_c for disorder are studied. The systems studied range from simple elastic systems with D_c=4 to systems with long range interactions with D_c=2 and systems with D_c=3 such as the vortex lattice with dispersive elastic constants. These problems are studied using the Gaussian Variational method and the Functional Renormalisation Group. In all the cases studied we find a typical ultra-slow loglog(x) growth of the asymptotic displacement correlation function, resulting in nearly perfect translational order. Consequences for the Bragg glass phase of vortex lattices are discussed.Comment: 12 RevTex pages, uses epsfig, 2 figure

Non-Abelian bosonization of the frustrated antiferromagnetic spin-1/2 chain

We study the spin-1/2 chain with nearest neighbor ($\kappa_1$) and next-nearest neighbor ($\kappa_2$) interactions in the regime $\kappa_2\gg \kappa_1$, which is equivalent to two chains with a `zig-zag' interaction. In the continuum limit, this system is described in term of two coupled level-1 WZW field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used to investigate the opening of a gap as a function of $\kappa_1$ and the associated spontaneous breakdown of parity. We calculate the dynamic spin structure factor near the wavevectors accessible to the continuum limit. We comment on the nonzero string order parameter and show the presence of a hidden ${\Bbb Z}_2\times{\Bbb Z}_2$ symmetry via a nonlocal transformation on the microscopic Hamiltonian. For a ferromagnetic interchain coupling, the model is conjectured to be critical, with different velocities for the spin singlet and spin triplet excitations.Comment: 20 pages, RevTeX, 1 postscript figure. Minor corrections added, resulting in different velocity renormalizations; no qualitative change in conclusion

Large-UU limit of a Hubbard model in a magnetic field: chiral spin interactions and paramagnetism

We consider the large-$U$ limit of the one-band Hubbard model at half-filling on a non-bipartite two-dimensional lattice. An external magnetic field can induce a three-spin chiral interaction at order $1 / U^2 ~$. We discuss situations in which, at low temperatures, the chiral term may have a larger effect than the Pauli coupling of electron spins to a magnetic field. We present a model which explicitly demonstrates this. The ground state is a singlet with a gap; hence the spin susceptibility is zero while the chiral susceptibility is finite and paramagnetic.Comment: 12 pages, plain TeX, one figure available on request, to appear in Phys. Rev.

Coupled Ladders in a Magnetic Field

We investigate the phase transitions in two-leg ladders systems in the incommensurate phase, for which the gap is destroyed by a magnetic field ($h_{c1}< h$) and the ladder is not yet totally saturated ($h < h_{c2}$). We compute quantitatively the correlation functions as a function of the magnetic field for an isolated strong coupling ladder $J_\perp \gg J_\parallel$ and use it to study the phase transition occuring in a three dimensional array of antiferromagnetically coupled ladders. The three dimensional ordering is in the universality class of Bose condensation of hard core bosons. We compute the critical temperature $T_c(h)$ as well as various physical quantities such as the NMR relaxations rate. $T_c$ has an unusual camel-like shape with a local minimum at $h=(h_{c1}+h_{c2})/2$ and behaves as $T_c \sim (h-h_{c1})^{2/3}$ for $h\sim h_{c1}$. We discuss the experimental consequences for compounds such as Cu_2(C_5H_{12}N_2)_2Cl_4Comment: 11 pages; some misprints corrected + one reference added; to appear in PR

Cyclotron resonance of correlated electrons in semiconductor heterostructures

The cyclotron resonance absorption of two-dimensional electrons in semiconductor heterostructures in high magnetic fields is investigated. It is assumed that the ionized impurity potential is a dominant scattering mechanism, and the theory explicitly takes the Coulomb correlation effect into account through the Wigner phonons. The cyclotron resonance linewidth is in quantitative agreement with the experiment in the Wigner crystal regime at T=4.2K. Similar to the cyclotron resonance theory of the charge density waves pinned by short-range impurities, the present results for the long-range scattering also show the doubling of the resonance peaks. However, unlike the case of the charge density waves, our theory gives the pinning mode independent of the bulk compressibility of the substrate materials.Comment: 6 pages, 5 figure

Instabilities in Luttinger liquids

We discuss the appearance of magnetic and charge instabilities, named respectively metamagnetism (MM) and phase separation (PS), in systems which can be described by a perturbed Luttinger liquid. We argue that such instabilities can be associated with the vanishing of the effective Fermi velocity v, which in some cases coincides with a divergence of the effective Luttinger parameter K. We analyze in particular an XXZ chain with next-nearest-neighbor interactions in different limits where MM shows up and an extended Hubbard model where in turn, PS occurs. Qualitative agreement with previous studies is found.Comment: 7 pages, 3 figure