Binding of Holes to Magnetic Impurities in a Strongly Correlated System

The effect of a magnetic (S=1/2) impurity coupled to a 2D system of correlated electrons (described by the t--J model) is studied by exact diagonalisations. It is found that, if the exchange coupling of the impurity with the neighboring spins is ferromagnetic or weakly antiferromagnetic, an extra hole can form bound states of different spatial symmetries with the impurity extending to a few lattice spacings. The binding energy is maximum when the impurity is completely decoupled (vacancy) and vanishes for an antiferromagnetic coupling exceeding $\sim 0.3 J$. Several peaks appear in the single hole spectral function below the lower edge of the quasiparticle band as signatures of the d-, s- and p-wave boundstates.Comment: Latex 11 pages, postscript files in uuencoded form, report# LPQTH-94/

Entanglement spectra of quantum Heisenberg ladders

Bipartite entanglement measures are fantastic tools to investigate quantum phases of correlated electrons. Here, I analyze the entanglement spectrum of **gapped** two-leg quantum Heisenberg ladders on a periodic ribbon partitioned into two identical periodic chains. Comparison of various entanglement entropies proposed in the literature is given. The entanglement spectrum is shown to closely reflect the low-energy gapless spectrum of each individual edge, for any sign of the exchange coupling constants. This extends the conjecture initially drawn for Fractional Quantum Hall systems to the field of quantum magnetism, stating a direct correspondence between the low-energy entanglement spectrum of a partitioned system and the true spectrum of the "virtual edges". A mapping of the reduced density matrix to a thermodynamic density matrix is also proposed via the introduction of an effective temperature.Comment: Revised version, 9 pages, 7 figures. "Supplementary material" showing additional results for **frustrated** ladder

Properties of holons in the Quantum Dimer Model

I introduce a doped two-dimensional quantum dimer model describing a doped Mott insulator and retaining the original Fermi statistics of the electrons. This model shows a rich phase diagram including a d-wave hole-pair unconventional superconductor at small enough doping and a bosonic superfluid at large doping. The hole kinetic energy is shown to favor binding of topological defects to the bare fermionic holons turning them into bosons, in agreement with arguments based on RVB wave-functions. Results are discussed in the context of cuprates superconductors.Comment: 4 pages, 5 figures, extensive revision, important new data included in Fig.4(a

Investigation of the chiral antiferromagnetic Heisenberg model using PEPS

A simple spin-$1/2$ frustrated antiferromagnetic Heisenberg model (AFHM) on the square lattice - including chiral plaquette cyclic terms - was argued [Anne E.B. Nielsen, German Sierra and J. Ignacio Cirac, Nature Communications $\bf 4$, 2864 (2013)] to host a bosonic Kalmeyer-Laughlin (KL) fractional quantum Hall ground state [V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett. $\bf 59$, 2095 (1987)]. Here, we construct generic families of chiral projected entangled pair states (chiral PEPS) with low bond dimension ($D=3,4,5$) which, upon optimization, provide better variational energies than the KL ansatz. The optimal $D=3$ PEPS exhibits chiral edge modes described by the Wess-Zumino-Witten $SU(2)_1$ model, as expected for the KL spin liquid. However, we find evidence that, in contrast to the KL state, the PEPS spin liquids have power-law dimer-dimer correlations and exhibit a gossamer long-range tail in the spin-spin correlations. We conjecture that these features are genuine to local chiral AFHM on bipartite lattices.Comment: 6 pages, 5 figures, Phys. Rev. B Rapid Com. (in press

Resonant Impurity Scattering in a Strongly Correlated Electron Model

Scattering by a single impurity introduced in a strongly correlated electronic system is studied by exact diagonalization of small clusters. It is shown that an inert site which is spinless and unable to accomodate holes can give rise to strong resonant scattering. A calculation of the local density of state reveals that, for increasing antiferromagnetic exchange coupling, d, s and p-wave symmetry bound states in which a mobile hole is trapped by the impurity potential induced by a local distortion of the antiferromagnetic background successively pull out from the continuum.Comment: 10 pages, 4 figures available on request, report LPQTH-93-2

The Gap Function Phi(k,w) for a Two-leg t-J Ladder and the Pairing Interaction

The gap function phi(k,omega), determined from a Lanczos calculation for a doped 2-leg t-J ladder, is used to provide insight into the spatial and temporal structure of the pairing interaction. It implies that this interaction is a local near-neighbor coupling which is retarded. The onset frequency of the interaction is set by the energy of an S=1 magnon-hole-pair and it is spread out over a frequency region of order the bandwith

Quantum critical phase with infinite projected entangled paired states

A classification of SU(2)-invariant Projected Entangled Paired States (PEPS) on the square lattice, based on a unique site tensor, has been recently introduced by Mambrini et al.~\cite{Mambrini2016}. It is not clear whether such SU(2)-invariant PEPS can either i) exhibit long-range magnetic order (like in the N\'eel phase) or ii) describe a genuine quantum critical point (QCP) or quantum critical phase (QCPh) separating two ordered phases. Here, we identify a specific family of SU(2)-invariant PEPS of the classification which provides excellent variational energies for the $J_1-J_2$ frustrated Heisenberg model, especially at $J_2=0.5$, corresponding to the approximate location of the QCP or QCPh separating the N\'eel phase from a dimerized phase. The PEPS are build from virtual states belonging to the $\frac{1}{2}^{\otimes N} \oplus 0$ SU(2)-representation, i.e. with $N$ "colors" of virtual \hbox{spin-$\frac{1}{2}$}. Using a full update infinite-PEPS approach directly in the thermodynamic limit, based on the Corner Transfer Matrix renormalization algorithm supplemented by a Conjugate Gradient optimization scheme, we provide evidence of i) the absence of magnetic order and of ii) diverging correlation lengths (i.e. showing no sign of saturation with increasing environment dimension) in both the singlet and triplet channels, when the number of colors $N\ge 3$. We argue that such a PEPS gives a qualitative description of the QCP or QCPh of the $J_1-J_2$ model.Comment: 11 pages, 13 figures, supplementary material as a zip file in source package, v4: minor adds to text + Table I and Appendix D (with 1 figure) adde

Competing Valence Bond Crystals in the Kagome Quantum Dimer Model

The singlet dynamics which plays a major role in the physics of the spin-1/2 Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model which originates from the latter NNVB-projected Heisenberg model via a non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalisation on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously-found 36-site Valence Bond Crystal (VBC) in fact competes with a new type of 12-site "{\it resonating-columnar}" VBC. The exceptionally large degeneracy of the GS multiplets (144 on our 108-site cluster) might reflect the proximity of the Z_2 dimer liquid. Interestingly, these two VBC "emerge" in {\it different topological sectors}. Implications for the interpretation of numerical results on the QHAF are outlined.Comment: 8 pages, 5 figures, 4 tables; Figure 2 and Table II update

Thermodynamic properties of the coupled dimer system Cu2_2(C5_5H12_{12}N2_2)2_2Cl4_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 [Cl\'emancey {\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.Comment: published version with minor change