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This work implements a variational determination of the elements of two-electron reduced density matrices corresponding to the ground and excited states of N-electron interacting systems based on the dispersion operator technique. The procedure extends the previously reported proposal [Nakata et al., J. Chem. Phys. 125, 244109 (2006)] to two-particle interaction Hamiltonians and N-representability conditions for the two-, three-, and four-particle reduced density matrices in the doubly occupied configuration interaction space. The treatment has been applied to describe electronic spectra using two benchmark exactly solvable pairing models: reduced Bardeen–Cooper–Schrieffer and Richardson–Gaudin–Kitaev Hamiltonians. The dispersion operator combined with N-representability conditions up to the four-particle reduced density matrices provides excellent results., Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

This work incorporates translational and reflection symmetry reductions to the variational determination of the two-particle reduced density matrix (2-RDM) corresponding to the ground state of N-particle systems, within the doubly occupied configuration interaction (DOCI) space. By exploiting these symmetries within this lower-bound variational methodology it is possible to treat larger systems than those previously studied. The 2-RDM matrix elements are calculated by imposing up to four-particle N-representability constraint conditions using standard semidefinite programing algorithms. The method is applied to the one- and two-dimensional XXZ spin 1/2 model of quantum magnetism. Several observables including the energy and the spin–spin correlation functions are obtained to assess the physical content of the variationally determined 2-RDM. Comparison with quantum-Monte Carlo and matrix product state simulations shows that in most cases only requiring up to three-particle positivity conditions is enough to correctly describe the ground-state properties of these one- and two-dimensional models.

15 pags., 4 figs., 2 apps., We derive the exact solution of a system of N-level atoms in contact with a Markovian reservoir. The resulting Liouvillian expressed in a vectorized basis is mapped to an SU(N) trigonometric Richardson-Gaudin model whose exact solution is given by a set of non-linear coupled equations. For N = 2 (SU(2)) we recover the exact solution of (2019 Phys. Rev. Lett. 122 010401). We then study the SU(3) case for three-level atom systems and discuss the properties of the steady state and dissipative gaps for finite systems as well as for the thermodynamic limit., J.D. and A.R. acknowledges financial support from the Spanish Ministerio de Ciencia, Innovaci´on y Universidades and the European regional development fund (FEDER), Project No. PGC2018-094180-B-I00. S.L.-H. acknowledges financial support from Mexican CONACyT project CB2015-01/255702. This collaboration has been supported by the Spanish Grant I-COOP2017 Ref:COOPB20289.

5 pags., 5 figs., Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can emerge in the bulk of the system whenever the local potential is varied in space, even if it does not cause a phase transition. In optical lattice implementations the overall harmonic potential that traps the atoms provides the boundaries of the topological phase that supports the edge currents, as well as providing the potential gradient across the topological phase that gives rise to the bulk current. Both the edge and bulk currents are resilient to several experimental parameters such as trapping potential, temperature, and disorder. We propose to investigate the properties of these currents directly from time-of-flight images with both short-time and long-time expansions., This work was supported by the EPSRC Grant No. EP/R020612/1; Spanish Projects PGC2018-094792-B-I00 (MCIU/AEI/FEDER, EU), PGC2018-094180-B-I00 (MCIU /AEI/FEDER, EU), and FIS2015-63770-P (MINECO /FEDER, EU); CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM), and CSIC Research Platform PTI-001.

10 pags., 7 figs., The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called PQGT N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained., A.R. and J.D. acknowledge the financial support of the Spanish Ministerio de Economıá y Competitividad and the European regional development fund (FEDER) under Projects No. FIS2015-63770-P. D.R.A. acknowledges financial support of the Consejo Nacional de Investigaciones Cientıfícas y Tećnicas under Grants Nos. PIP 11220130100377CO and 2013- 1401PCB and of the Agencia Nacional de Promocioń Cientıfíca y Tecnológica, Argentina under Grant No. PICT-201-0381. P.C. acknowledges financial support of the Consejo Nacional de Investigaciones Cientıfícas y Tećnicas under Grant. No. PIP 11220150100442CO. D.R.A. and P.C. acknowledge financial support of the Universidad de Buenos Aires under Grant No. 20020150100157BA.

This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D. R. Alcoba et al., J. Chem. Phys. 149, 194105 (2018)] as well as with the exact DOCI values. We apply the different approximations to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method. The numerical results show the usefulness of our treatment to achieve a high degree of accuracy., Facultad de Ciencias Exactas, Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

10 pags., 8 figs., 1 tab., 1 app., We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localized bulk states deep in their valence and conduction bands. These states manifest when local potential gradients are applied to the bulk, while all parts of the system remain adiabatically connected to the same phase. In turn, the bulk states produce bulk current transverse to the potential difference. This occurs even when the potential is always below the energy gap, where one expects only edge currents to appear. Bulk currents are topologically protected and behave as edge currents under an external influence, such as temperature or local disorder. Detecting topologically resilient bulk currents offers a direct means to probe the localized bulk states., This work was supported by the EPSRC Grant No. EP/R020612/1, Spanish Projects No. PGC2018-094792-B-I00 (MCIU/AEI/FEDER, EU), No. PGC2018-094180-B-I00 (MCIU/AEI/FEDER, EU), No. FIS2015-63770-P (MINECO/FEDER, EU), CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM), and CSIC Research Platform PTI-001.

Ground-state energies and two-particle reduced density matrices (2-RDMs) corresponding to

11 pags., 6 figs., 5 tabs., 2 apps., Ground-state energies and two-particle reduced density matrices (2-RDMs) corresponding to N-particle systems are computed variationally within the doubly occupied configuration interaction (DOCI) space by constraining the 2-RDM to satisfy a complete set of three-particle N-representability conditions known as three-positivity conditions. These conditions are derived and implemented in the variational calculation of the 2-RDM with standard semidefinite programming algorithms. Ground state energies and 2-RDMs are computed for N2, CO, CN−, and NO+ molecules at both equilibrium and nonequilibrium geometries as well as for pairing models at different repulsive interaction strengths. The results from the full three-positivity conditions are compared with those from the exact DOCI method and with approximated 2-RDM variational ones obtained within two-positivity and two-positivity plus a subset of three-positivity conditions, as recently reported [D. R. Alcoba et al., J. Chem. Phys. 148, 024105 (2018) and A. Rubio-Garc´ıa et al., J. Chem. Theory Comput. 14, 4183 (2018)]. The accuracy of these numerical determinations and their low computational cost demonstrate the usefulness of the three-particle variational constraints within the DOCI framework. Published by AIP Publishing., The authors acknowledge financial support from the Universidad de Buenos Aires (Grant No. 20020150100157BA), the Consejo Nacional de Investigaciones Cientıficas y Tecnicas (Grant Nos. PIP 11220130100377CO, PIP ´ 11220130100311CO, 11220150100442CO, and 2013-1401- PCB), the Agencia Nacional de Promocion Cientfica y Tecnologica, Argentina (Grant No. PICT-201-0381), and the ´ Spanish Ministerio de Economıa y Competitividad and the European regional development fund (FEDER) (No. FIS2015- 63770-P).

9 pags., 6 figs., Ultracold atom experiments allow the study of topological insulators, such as the non-interacting Haldane model. In this work we study a generalization of the Haldane model with spin¿spin on-site interactions that can be implemented on such experiments. We focus on measuring the winding number, a topological invariant, of the ground state, which we compute using a mean-field calculation that effectively captures long-range correlations and a matrix product state computation in a lattice with 64 sites. Our main result is that we show how the topological phases present in the non-interacting model survive until the interactions are comparable to the kinetic energy. We also demonstrate the accuracy of our mean-field approach in efficiently capturing long-range correlations. Based on state-of-the-art ultracold atom experiments, we propose an implementation of our model that can give information about the topological phases., This work has been supported by Spanish MINECO Projects FIS2015-70856-P and FIS2015-63770-P (both co financed by FEDER funds) and CAMPRICYT Project QUITEMAD+S2013/ICE-2801. The authors acknowledge the computer resources and technical assistance provided by the Centro de Supercomputación y Visualización de Madrid (CeSViMa).