arXiv subjects

S. Capponi

Publications and source records attributed to S. Capponi.

At least 37 records · Page 2Linked to original sources

arXiv2010

Entanglement of quantum spin systems: a valence-bond approach

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.

cond-mat.str-el↗

arXiv2010

Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain

The zero-temperature properties of the SO(5) bilinear-biquadratic Heisenberg spin chain are investigated by means of a low-energy approach and large scale numerical calculations. In sharp contrast to the spin-1 SO(3) Heisenberg chain, we show that the SO(5) Heisenberg spin chain is dimerized with a two-fold degenerate ground state. On top of this gapful phase, we find the emergence of a non-degenerate gapped phase with hidden (Z$_2$ $\times$ Z$_2$)$^2$ symmetry and spin-3/2 edge states that can be understood from a SO(5) AKLT wave function. We derive a low-energy theory describing the quantum critical point which separates these two gapped phases. It is shown and confirmed numerically that this quantum critical point belongs to the SO(5)$_1$ universality class.

cond-mat.str-el↗

arXiv2010

Competing orders in the generalized Hund chain model at half-filling

By using a combination of several non-perturbative techniques -- a one-dimensional field theoretical approach together with numerical simulations using density matrix renormalization group -- we present an extensive study of the phase diagram of the generalized Hund model at half-filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin 3/2, other cold gases like Ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg Hubbard ladder with interchain hopping. Our results obtained from a weak coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.

cond-mat.str-el↗

arXiv2010

Asymmetric spin-1/2 two-leg ladders

We consider asymmetric spin-1/2 two-leg ladders with non-equal antiferromagnetic (AF) couplings J_|| and κJ_|| along legs (κ<= 1) and ferromagnetic rung coupling, J_\perp. This model is characterized by a gap Δin the spectrum of spin excitations. We show that in the large J_\perp limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at κ=1, admits a linear scaling for the spin gap Δ~ J_\perp. The second class appears for a strong asymmetry of the coupling along legs, κJ_|| << J_\perp << J_|| and is characterized by two energy scales: the exponentially small spin gap Δ~ J_\perp \exp(-J_|| / J_\perp), and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ~ J_\perp^2 /J_|| . We report numerical results obtained by exact diagonalization, density matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetry. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.

cond-mat.str-el↗

arXiv2010

Quantum phase transitions in three-leg spin tubes

We investigate the properties of a three-leg quantum spin tube using several techniques such as the density matrix renormalization group method, strong coupling approaches and the non linear sigma model. For integer spins S, the model proves to exhibit a particularly rich phase diagram consisting of an ensemble of 2S phase transitions. They can be accurately identified by the behavior of a non local string order parameter associated to the breaking of a hidden symmetry in the Hamiltonian. The nature of these transitions are further elucidated within the different approaches. We carry a detailed DMRG analysis in the specific cases S = 1. The numerical data confirm the existence of two Haldane phases with broken hidden symmetry separated by a trivial singlet state. The study of the gap and of the von Neumann entropy suggest a first order phase transition but at the close proximity of a tricritical point separating a gapless and a first order transition line in the phase diagram of the quantum spin tube.

cond-mat.str-el↗

arXiv2010

Haldane charge conjecture in one-dimensional multicomponent fermionic cold atoms

A Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and gapped phases depending on the parity of $N$ for attractive interactions at half-filling. The analogue of the Haldane phase of the spin-1 Heisenberg chain is stabilized for N=2 with non-local string charge correlation, and pseudo-spin 1/2 edge states. At the heart of this even-odd behavior is the existence of a spin-singlet pseudo-spin $N/2$ operator which governs the low-energy properties of the model for attractive interactions and gives rise to the Haldane physics.

cond-mat.str-el↗

arXiv2009

Three-Component Fermi Gas in a one-dimensional Optical Lattice

We investigate the effect of the anisotropy between the s-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the 2$k_F$ atomic density waves fluctuations of the three species. At small enough densities or strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally our results are discussed in light of a recent experiment on $^{6}$Li atoms.

cond-mat.str-el↗

arXiv2009

Theory of the Raman spectra of the Shastry-Sutherland antiferromagnet SrCu$_2$(BO$_3$)$_2$ doped with nonmagnetic impurities

Controlled doping of SrCu$_2$(BO$_3$)$_2$, a faithful realization of the Heisenberg spin-1/2 antiferromagnet on the Shastry-Sutherland lattice, with non-magnetic impurities generates bound-states below the spin gap. These bound-states and their symmetry properties are investigated by exact diagonalisation of small clusters and within a simple effective model describing a spinon submitted to an attractive extended potential. It is shown that Raman spectroscopy is a unique technique to probe these bound-states. Quantitative theoretical Raman spectra are numerically obtained.

cond-mat.str-el↗

arXiv2008

Spin 3/2 fermions with attractive interactions in a one-dimensional optical lattice: phase diagrams, entanglement entropy, and the effect of the trap

We study spin 3/2 fermionic cold atoms with attractive interactions confined in a one-dimensional optical lattice. Using numerical techniques, we determine the phase diagram for a generic density. For the chosen parameters, one-particle excitations are gapped and the phase diagram is separated into two regions: one where the two-particle excitation gap is zero, and one where it is finite. In the first region, the two-body pairing fluctuations (BCS) compete with the density ones. In the other one, a molecular superfluid (MS) phase, in which bound-states of four particles form, competes with the density fluctuations. The properties of the transition line between these two regions is studied through the behavior of the entanglement entropy. The physical features of the various phases, comprising leading correlations, Friedel oscillations, and excitation spectra, are presented. To make the connection with experiments, the effect of a harmonic trap is taken into account. In particular, we emphasize the conditions under which the appealing MS phase can be realized, and how the phases could be probed by using the density profiles and the associated structure factor. Lastly, the consequences on the flux quantization of the different nature of the pairing in the BCS and MS phases are studied in a situation where the condensate is in a ring geometry.

cond-mat.str-el↗

arXiv2008

Effective Theory of Magnetization Plateaux in the Shastry-Sutherland Lattice

We use the non-perturbative Contractor-Renormalization method (CORE) in order to derive an effective model for triplet excitations on the Shastry-Sutherland lattice. For strong enough magnetic fields, various magnetization plateaux are observed, e.g. at 1/8, 1/4, 1/3 of the saturation, as found experimentally in a related compound. Moreover, other stable plateaux are found at 1/9, 1/6 or 2/9. We give a critical review of previous works and try to resolve some apparent inconsistencies between various theoretical approaches.

cond-mat.str-el↗

arXiv2008

Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material

The phase diagram in temperature and magnetic field of the metal-organic, two-leg, spin-ladder compound (C5H12N)2CuBr4 is studied by measurements of the specific heat and the magnetocaloric effect. We demonstrate the presence of an extended spin Luttinger-liquid phase between two field-induced quantum critical points and over a broad range of temperature. Based on an ideal spin-ladder Hamiltonian, comprehensive numerical modelling of the ladder specific heat yields excellent quantitative agreement with the experimental data across the complete phase diagram.

cond-mat.str-el↗

arXiv2008

Trionic and quartetting phases in one-dimensional multicomponent ultracold fermions

We investigate the possible formation of a molecular condensate, which might be, for instance, the analogue of the alpha condensate of nuclear physics, in the context of multicomponent cold atoms fermionic systems. A simple paradigmatic model of N-component fermions with contact interactions loaded into a one-dimensional optical lattice is studied by means of low-energy and numerical approaches. For attractive interaction, a quasi-long-range molecular superfluid phase, formed from bound-states made of N fermions, emerges at low density. We show that trionic and quartetting phases, respectively for N=3,4, extend in a large domain of the phase diagram and are robust against small symmetry-breaking perturbations.

cond-mat.str-el↗

arXiv2008

Molecular superfluid phase in systems of one-dimensional multicomponent fermionic cold atoms

We study a simple model of N-component fermions with contact interactions which describes fermionic atoms with N=2F+1 hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for attractive interaction, a quasi-long-range molecular superfluid phase emerges at low density. In such a phase, the pairing instability is strongly suppressed and the leading instability is formed from bound-states made of N fermions. At small density, the molecular superfluid phase is generic and exists for a wide range of attractive contact interactions without an SU(N) symmetry between the hyperfine states.

cond-mat.str-el↗

arXiv2008

Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points

We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. Based on an algorithmic idea by Henley, we simulate a stochastic process of classical dimer configurations in continuous time and perform a stochastic analytical continuation to obtain the dynamical correlations in momentum space and the frequency domain. This approach allows us to observe directly the dispersion relations and the evolution of the spectral intensity within the Brillouin zone beyond the single-mode approximation. On the square lattice, we confirm analytical predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0) and further reveal the existence of shadow bands close to the wavevector (0,0). On the cubic lattice the spectrum is also gapless but here only a single soft mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The soft mode has a quadratic dispersion at very long wavelength, but crosses over to a linear behavior very rapidly. We believe this to be the remnant of the linearly dispersing "photon" of the Coulomb phase. Finally the triangular lattice is in a fully gapped liquid phase where the bottom of the dimer spectrum exhibits a rich structure. At the M point the gap is minimal and the spectral response is dominated by a sharp quasiparticle peak. On the other hand, at the X point the spectral function is much broader. We sketch a possible explanation based on the crossing of the coherent dimer excitations into the two-vison continuum.

cond-mat.stat-mech↗

arXiv2007

Contractor-Renormalization approach to frustrated magnets in magnetic field

We propose to use the Contractor Renormalization (CORE) technique in order to derive effective models for quantum magnets in a magnetic field. CORE is a powerful non-perturbative technique that can reduce the complexity of a given microscopic model by focusing on the low-energy part. We provide a detailed analysis of frustrated spin ladders which have been widely studied in the past: in particular, we discuss how to choose the building block and emphasize the use of their reduced density matrix. With a good choice of basis, CORE is able to reproduce the existence or not of magnetization plateaux in the whole phase diagram contrary to usual perturbation theory. We also address the issue of plateau formation in two-dimensional bilayers and point out the analogy between non-frustrated strongly anisotropic models and frustrated SU(2) ones.

cond-mat.str-el↗

arXiv2007

Breathers and Raman scattering in a two-leg ladder with staggered Dzialoshinskii-Moriya interaction

Recent experiments have revealed the role of staggered Dzialoshinskii-Moriya interaction in the magnetized phase of an antiferromagnetic spin 1/2 two-leg ladder compound under a uniform magnetic field. We derive a low energy effective field theory describing a magnetized two-leg ladder with a weak staggered Dzialoshinskii-Moriya interaction. This theory predicts the persistence of the spin gap in the magnetized phase, in contrast to standard two-leg ladders, and the presence of bound states in the excitation spectrum. Such bound states are observable in Raman scattering measurements. These results are then extended to intermediate Dzialoshinskii-Moriya interaction using Exact Diagonalizations.

cond-mat.str-el↗

arXiv2007

Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder: a quantum Monte Carlo study

We consider a spin-1/2 ladder with a ferromagnetic rung coupling J_\perp and inequivalent chains. This model is obtained by a twist (θ) deformation of the ladder and interpolates between the isotropic ladder (θ=0) and the SU(2) ferromagnetic Kondo necklace model (θ=π). We show that the ground state in the (θ,J_\perp) plane has a finite string order parameter characterising the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from Δ/J_\| \propto J_\perp/J_\| for θ< θ_c \simeq 8π/9 to Δ/J_\| \propto (J_\perp/J_\|)^2 for θ> θ_c. Those results are obtained on the basis of large scale Quantum Monte Carlo calculations.

cond-mat.str-el↗

arXiv2007

Thermodynamic properties of the coupled dimer system Cu$_2$(C$_5$H$_{12}$N$_2$)$_2$Cl$_4$

We re-examine the thermodynamic properties of the coupled dimer system Cu$_2$(C$_5$H$_{12}$N$_2$)$_2$Cl$_4$ under magnetic field in the light of recent NMR experiments [Clémancey {\it et al.}, Phys. Rev. Lett. {\bf 97}, 167204 (2006)] suggesting the existence of a finite Dzyaloshinskii-Moriya interaction. We show that including such a spin anisotropy greatly improves the fit of the magnetization curve and gives the correct trend of the insofar unexplained anomalous behavior of the specific heat in magnetic field at low temperature.

cond-mat.str-el↗