arXiv subjects

Sylvain Capponi

Publications and source records attributed to Sylvain Capponi.

At least 37 records · Page 2Linked to original sources

arXiv2021

Quantum half-orphans in kagome antiferromagnets

We numerically study the effects of non-magnetic impurities (vacancies) in the spin-$S$ Heisenberg antiferromagnet on the kagomé lattice. For a range of low but nonzero temperatures, and spin values that extend down to $S=2$, we find that the magnetization response to an external magnetic field is consistent with the response of emergent "half-orphan" degrees of freedom that are expected to dominate the response of the corresponding classical magnet in a similar temperature range whenever there are two vacancies on the same triangle. Specifically, for all spin values we have considered (from $S=1/2$ to $S=4$), there is a large enhancement of the local susceptibility of the lone spin on such a triangle with two vacancies; in the presence of a uniform magnetic field $h$, this lone-spin behaves effectively as an almost free spin $S$ in an effective field $h/2$. Quite remarkably, in the zero temperature limit, the ground state in the presence of a half-orphan has a non-zero total spin value $S_{GS}$ that shows a trend similar to $S/2$ when $S\ge 2$. These qualitative aspects of the response differ strikingly from the more conventional response of diluted samples without such half-orphan degrees of freedom. We discuss how these findings could be checked experimentally.

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arXiv2020

Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice

We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (ie self-conjugate $\bf 6$ representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimer-like phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauthé, S. Capponi and D. Poilblanc, Phys. Rev. B $\textbf{99}$, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric Projected Entangled Pair States (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalisation (ED) and density matrix renormalisation group (DMRG) calculations.

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arXiv2020

Ground-state properties of the one-dimensional Hubbard model with pairing potential

We consider a modification of the one-dimensional Hubbard model by including an external pairing potential. Guided by analytic bosonization results, we quantitatively determine the grand-canonical zero-temperature phase diagram using both finite and infinite density matrix renormalization group algorithm based on the formalism of matrix product states and matrix product operator, respectively. By computing various local quantities as well as the half-system entanglement, we are able to distinguish between Mott, metallic and superconducting phases. We point out the compressible nature of the Mott phase and the fully gapped nature of the many-body spectrum of the superconducting phase, in the presence of explicit U(1)-charge symmetry breaking.

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arXiv2020

SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS

Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projected Entangled Pair States (PEPS). Guided by extensive exact diagonalization and density matrix renormalization group calculations, we construct an optimized symmetric PEPS for a SU$(3)_1$ chiral spin liquid on the square lattice. Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. In all three $\mathbb{Z}_3$ sectors, the level counting of the linear dispersing modes is in full agreement with SU$(3)_1$ Wess-Zumino-Witten conformal field theory prediction. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence. Possible universal properties of topological SU$(N)_k$ chiral PEPS are discussed.

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arXiv2019

Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins

Chiral Haldane phases are examples of one-dimensional topological states of matter which are protected by projective SU($N$) group (or its subgroup $\mathbb{Z}_N \times \mathbb{Z}_N$) with $N>2$. The unique feature of these symmetry protected topological (SPT) phases is that they are accompanied by inversion-symmetry breaking and the emergence of different left and right edge states which transform, for instance, respectively in the fundamental ($\boldsymbol{N}$) and anti-fundamental ($\overline{\boldsymbol{N}}$) representations of SU($N$). We show, by means of complementary analytical and numerical approaches, that these chiral SPT phases as well as the non-chiral ones are realized as the ground states of a generalized two-leg SU($N$) spin ladder in which the spins in the first chain transform in $\boldsymbol{N}$ and the second in $\overline{\boldsymbol{N}}$. In particular, we map out the phase diagram for $N=3$ and $4$ to show that {\em all} the possible symmetry-protected topological phases with projective SU($N$)-symmetry appear in this simple ladder model.

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arXiv2019

NMR relaxation in the spin-1 Heisenberg chain

We consider the isotropic $S=1$ Heisenberg chain with a finite Haldane gap $Δ$ and use state-of-the-art numerical techniques to investigate its dynamical properties at finite temperature, focusing on the nuclear spin-lattice relaxation rate $1/T_1$ measured in nuclear magnetic resonance (NMR) experiments for instance. In particular, we analyze the contributions from modes with momenta close to $q\approx 0$ and $q\approx π$ as a function of temperature. At high-temperature, we observe spin diffusion with a non-trivial exponent. At low-temperature, we argue that a simple activated behavior $1/T_1 \propto\exp(-Δ/T)$ can only be observed at temperatures much smaller than the gap $Δ$.

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arXiv2019

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the $J_1-J_2$ frustrated Heisenberg model.For $J_2/J_1\sim 0.55$ we show the emergence of critical (algebraic) dimer-dimer correlations -- typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices -- while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.

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arXiv2019

SU(4) topological RVB spin liquid on the square lattice

We generalize the construction of the spin-1/2 SU(2) Resonating Valence Bond (RVB) state to the case of the self-conjugate $\bf 6$-representation of SU(4). As for the case of SU(2) [J-Y. Chen and D. Poilblanc, Phys. Rev. B $\textbf{97}$, 161107(R) (2018)], we use the Projected Entangled Pair State (PEPS) formalism to derive a simple (two-dimensional) family of generalized SU(4) RVB states on the square lattice. We show that, when longer-range SU(4)-singlet bonds are included, a local gauge symmetry is broken down from U(1) to $\mathbb{Z}_2$, leading to the emergence of a short-range spin liquid. Evidence for the topological nature of this spin liquid is provided by the investigation of the Renyi entanglement entropy of infinitely-long cylinders and of the modular matrices. Relevance to microscopic models and experiments of ultracold atoms is discussed.

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arXiv2018

Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets

Theoretically challenging, the understanding of the dynamical response in quantum antiferromagnets is of great interest, in particular for both inelastic neutron scattering (INS) and nuclear magnetic resonance (NMR) experiments. In such a context, we theoretically address this question for quasi-one-dimensional quantum magnets, e.g. weakly coupled spin chains for which many compounds are available in Nature. In this class of systems, the dimensional crossover between a three-dimensional ordered regime at low temperature towards one-dimensional physics at higher temperature is a non-trivial issue, notably difficult concerning dynamical properties. Here we present a comprehensive theoretical study based on both analytical calculations (bosonization + random phase and self-consistent harmonic approximations) and numerical simulations (quantum Monte Carlo + stochastic analytic continuation) which allows us to describe the full temperature crossover for the NMR relaxation rate $1/T_1$, from one-dimensional Tomonaga-Luttinger liquid physics to the three-dimensional ordered regime, as a function of inter-chain couplings. The dynamical structure factor, directly probing the INS intensity, is also computed in the different regimes.

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arXiv2018

Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study

Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the Fractional Quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the spin liquid analog of the (bosonic) non-Abelian Moore-Read FQH state, as suggested by Exact Diagonalisation of small clusters. Using families of fully SU(2)-spin symmetric and translationally invariant chiral Projected Entangled Pair States (PEPS), variational energy optimization is performed using infinite-PEPS methods, providing good agreement with Density Matrix Renormalisation Group (DMRG) results. A careful analysis of the bulk spin-spin and dimer-dimer correlation functions in the optimized spin liquid suggests that they exhibit long-range "gossamer tails". We argue these tails are finite-$D$ artifacts of the chiral PEPS, which become irrelevant when the PEPS bond dimension $D$ is increased. From the investigation of the entanglement spectrum, we observe sharply defined chiral edge modes following the prediction of the SU(2)$_2$ Wess-Zumino-Witten theory and exhibiting a conformal field theory (CFT) central charge $c=3/2$, as expected for a Moore-Read chiral spin liquid. We conclude that the PEPS formalism offers an unbiased and efficient method to investigate non-Abelian chiral spin liquids in quantum antiferromagnets.

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arXiv2018

Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model

Spontaneous discrete symmetry breaking can be described in the framework of Projected Entangled Pair States (PEPS) by linearly superposing local tensors belonging to two (or more) symmetry classes of tensors. This is illustrated in the case of a frustrated spin-1 Heisenberg model on the square lattice, which hosts a nematic spin liquid spontaneously breaking lattice $π/2$-rotation symmetry. A superposition of SU(2)-symmetric PEPS tensors belonging to two irreducible representations of the lattice point group is shown to capture accurately the properties of the nematic phase, as shown from a comparison to Exact Diagonalisations and Density Matrix Renormalization Group results.

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arXiv2018

Dynamical properties of the $S=\frac{1}{2}$ random Heisenberg chain

We use numerical techniques to study dynamical properties at finite temperature ($T$) of the Heisenberg spin chain with random exchange couplings, which realizes the random singlet (RS) fixed point in the low-energy limit. Specifically, we study the dynamic spin structure factor $S(q,ω)$, which can be probed directly by inelastic neutron scattering experiments and, in the limit of small $ω$, in nuclear magnetic resonance (NMR) experiments through the spin-lattice relaxation rate $1/T_1$. Our work combines three complementary methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Unlike the uniform system, whose low-energy excitations at low $T$ are restricted to $q$ close to $0$ and $π$, our study reveals a continuous narrow band of low-energy excitations in $S(q,ω)$, extending throughout the Brillouin zone. Close to $q=π$, the scaling properties of these excitations are well captured by the RS theory, but we also see disagreements with some aspects of the predicted $q$-dependence further away from $q=π$. Furthermore we find spin diffusion effects close to $q=0$ that are not contained within the RS theory but give non-negligible contributions to the mean $1/T_1$. To compare with NMR experiments, we consider the distribution of the local $1/T_1$ values, which is broad, approximately described by a stretched exponential. The mean value first decreases with $T$, but starts to increase and diverge below a crossover temperature. Although a similar divergent behavior has been found for the static uniform susceptibility, this divergent behavior of $1/T_1$ has never been seen in experiments. Our results show that the divergence of the mean $1/T_1$ is due to rare events in the disordered chains and is concealed in experiments, where the typical $1/T_1$ value is accessed.

cond-mat.str-el↗

arXiv2018

Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders

Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg SU($N$) spin ladders. Two-leg ladders provide a rich and highly non-trivial extension of the single chain case on the way towards the relatively little explored two dimensional situation. Focusing on the experimentally relevant limit of one fermion per site, antiferromagnetic exchange interactions, and $2\leq N \leq 6$, we show that the phase diagrams as a function of the interchain (rung) to intrachain (leg) coupling ratio $J_\perp/J_\Vert$ strongly differ for even vs. odd $N$. For even $N=4$ and 6, we demonstrate that the phase diagram consists of a single valence bond crystal (VBC) with a spatial period of $N/2$ rungs. For odd $N=3$ and 5, we find surprisingly rich phase diagrams exhibiting three distinct phases. For weak rung coupling, we obtain a VBC with a spatial period of $N$ rungs, whereas for strong coupling we obtain a critical phase related to the case of a single chain. In addition, we encounter intermediate phases for odd $N$, albeit of a different nature for $N=3$ as compared to $N=5$. For $N=3$, we find a novel gapless intermediate phase with $J_\perp$-dependent incommensurate spatial fluctuations in a sizeable region of the phase diagram. For $N=5$, there are strong indications for a narrow potentially gapped intermediate phase, whose nature is not entirely clear.

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arXiv2017

Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet

We study the dynamic spin structure factor of the spin-$1/2$ square-lattice Heisenberg antiferromagnet and of the $J$-$Q$ model (with 4-spin interactions $Q$ and Heisenberg exchange $J$). Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with QMC simulations, we can treat the sharp ($δ$-function) contribution from spinwaves (magnons) and a continuum at higher energy. The results for the Heisenberg model agree with neutron scattering experiments on Cu(DCOO)$_2$$\cdot$4D$_2$O, where a broad spectral-weight continuum at $q=(π,0)$ was interpreted as deconfined spinons. Our results at $(π,0)$ show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at $q=(π/2,π/2)$ (as also seen experimentally). Turning on $Q$, we observe a rapid reduction of the $(π,0)$ magnon weight to zero, well before the deconfined quantum phase transition into a spontaneously dimerized state. We re-interpret the picture of deconfined spinons at $(π,0)$ in the experiments as nearly deconfined spinons---a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile $(π,0)$-magnon in the Heisenberg model and its depletion in the $J$-$Q$ model, we introduce an effective model in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy with the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model reproduces the $(π,0)$ and $(π/2,π/2)$ features of the Heisenberg model. It can also account for the rapid loss of the $(π,0)$ magnon with increasing $Q$ and a remarkable persistence of a large magnon pole at $q=(π/2,π/2)$ even at the deconfined critical point.

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arXiv2017

Competing Bose-Glass physics with disorder-induced Bose-Einstein condensation in the doped $S=1$ antiferromagnet Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ at high magnetic fields

We study the interplay between disorder and interactions for emergent bosonic degrees of freedom induced by an external magnetic field in the Br-doped spin-gapped antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ (DTNX). Building on nuclear magnetic resonance experiments at high magnetic field [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017)], we describe the localization of isolated impurity states, providing a realistic theoretical modeling for DTNX. Going beyond single impurity localization we use quantum Monte Carlo simulations to explore many-body effects from which pairwise effective interactions lead to a (impurity-induced) BEC revival [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017)]. We further address the question of the existence of a many-body localized Bose-glass (BG) phase in DTNX, which is found to compete with a series of a new kind of BEC regimes made out of the multi-impurity states. The global magnetic field-temperature phase diagram of DTNX reveals a very rich structure for low impurity concentration, with consecutive disorder-induced BEC mini-domes separated by intervening many-body localized BG regimes. Upon increasing the impurity level, multiple mini-BEC phases start to overlap, while intermediate BG regions vanish.

cond-mat.str-el↗

arXiv2017

Weak Versus Strong Disorder Superfluid-Bose Glass Transition in One Dimension

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass-transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter $K_c$ takes its universal Giamarchi-Schulz value $K_{c}=3/2$. Conversely, a non-universal $K_c>3/2$ emerges for stronger attraction where weak-link physics is relevant. In this strong disorder regime, the transition is characterized by self-similar power-law distributed weak links with a continuously varying characteristic exponent $α$.

cond-mat.dis-nn↗

arXiv2017

Disorder-induced Revival of the Bose-Einstein Condensation in Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ at High Magnetic Fields

Building on recent NMR experiments [Phys. Rev. Lett. 118, 067203], we theoretically investigate the high magnetic field regime of the disordered quasi-one-dimensional $S=1$ antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$. The interplay between disorder, chemically controlled by Br-doping, interactions, and the external magnetic field, leads to a very rich phase diagram. Beyond the well-known antiferromagnetically ordered regime, analog of a Bose condensate of magnons, which disappears when $H\ge 12.3$ T, we unveil a resurgence of phase coherence at higher field $H\sim 13.6$ T, induced by the doping. Interchain couplings stabilize finite temperature long-range order whose extension in the field - temperature space is governed by the concentration of impurities $x$. Such a "mini-condensation" contrasts with previously reported Bose-glass physics in the same regime, and should be accessible to experiments.

cond-mat.str-el↗

arXiv2017

Nuclear Magnetic Resonance Reveals Disordered Level-Crossing Physics in the Bose-Glass Regime of the Br-doped Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ Compound at a High Magnetic Field

By measuring the nuclear magnetic resonance (NMR) 1/T_1 relaxation rate in the Br (bond) doped DTN compound, Ni(Cl(1-x)Br_x)2-4SC(NH2)2 (DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H* = 13.6 T. From its temperature and field dependence we conclude that this corresponds to a level crossing of the energy levels related to the doping-induced impurity states. Observation of the local NMR signal from the spin adjacent to the doped Br allowed us to fully characterize this impurity state. We have thus quantified a microscopic theoretical model that paves the way to better understanding of the Bose-glass physics in DTNX, as revealed in the related theoretical study [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017), arXiv:1610.05136].

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