"Grand Canonical" Finite Size Numerical Approaches : a Route to Measuring Bulk Properties under Applied Field

We exploit a prescription to observe directly the physical properties of the thermodynamic limit under continuously applied field in one-dimensional quantum finite lattice systems. By systematically scaling down the energy of the Hamiltonian of the open system from center toward both ends, one could adopt the edge sites with negligibly small energy scale as a "grand canonical" small particle bath, and an equilibrium states with non-integer arbitrary conserved numbers, e.g., electron numbers or sz, are realized in the main part of the system. This will enable the evaluation of the response functions under continuously varying external field in a small lattice without any fine tuning or scaling of parameters while keeping the standard numerical accuracy. Demonstrations are given on quantum spin systems as well as on a Hubbard model by the density matrix renormalization group calculation.Comment: 5pages, 3 figure

Fractional quantum Hall effects in graphene on a h-BN substrate

Fractional quantum Hall (FQH) effects in graphene are studied because of their relativistic characteristics and the valley degree of freedom. Recently FQH effects have been observed at various filling factors with graphene on a hexagonal boron nitride (h-BN) substrate. However, it is known that h-BN creates the mass term in the Dirac Hamiltonian that acts as the effective model of graphene. To understand recent experiments, we shall investigate many-body effects in the massive Dirac electron system. In this paper, we study the mass-term effects on the FQH states of Dirac electrons by exact diagonalization. We examine the ground state at filling factor 1/3 in the $n=\pm 1$ Landau level. Without the mass term, the ground state in the Laughlin state featuring valley degeneracy and the lowest excitation is characterized by the valley unpolarized state (known as the valley skyrmion state). Conversely, we find that the mass-term lifts the valley degeneracy due to the breaking of the inversion symmetry. We also demonstrate that the valley unpolarized excitation is suppressed and that the fully or partially polarized state appears in the lowest excitation by increasing the mass term. Finally, we discuss the stability of FQH states in the massive Dirac Hamiltonian in experimental situations. We find that our numerical results are in agreement with previous experimental results

Ground state phase diagram of 2D electrons in high magnetic field

The ground state phase diagram of two-dimensional electrons in high magnetic field is studied by the density matrix renormalization group (DMRG) method. The low energy excitations and pair correlation functions in Landau levels of N=0,1,2 are calculated for wide range of fillings. The obtained results for systems with up to 25 electrons confirm the existence of various electronic states in quantum Hall systems. The ground state phase diagram for N=0,1,2 consisting of incompressible liquids, compressible liquids, charge density waves called stripe, bubble and Wigner crystal is determined.Comment: 4 pages, 7 figures, Proceedings of EP2DS-15, to appear in Physica

Field Induced Quantum Phase Transitions in S=1/2S=1/2 J1J_1-J2J_2 Heisenberg Model on the Square Lattice

We study the magnetic field dependence of the ground state of $S=1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice by the DMRG method with the sine-square deformation. We obtain 8 different phases including plaquette valence-bond crystal with a finite spin gap, transverse N$\acute{\rm e}$el, transverse stripe, 1/2 magnetization plateau with up-up-up-down (uuud), and three new phases we named Y-like, V-like, and $\Psi$ phases around $J_2/J_1$ =0.55-0.6 depending on the magnetic field. The phase transitions to uuud and Y-like states from transverse N$\acute{\rm e}$el (at $J_2/J_1$ = 0.55) and stripe (at $J_2/J_1$ = 0.6) states are discontinuous, as in the case of spin-flop

Ground state phase diagram of twisted three-leg spin tube in magnetic field

We study the ground state phase diagram of the twisted three-leg spin tube in magnetic fields by the density matrix renormalization group (DMRG) method. The twisted spin tube is composed of triangular unit cells and possesses strong quantum fluctuations under geometrical frustration. We apply the sine square deformation method to remove the strong boundary effects and obtain smooth magnetization curves without steps of finite systems. With the analysis of the magnetization curves and correlation functions we determine the ground state phase diagram consisting of (a) a Tomonaga-Luttinger (TL) liquid characterized by spin-$\frac{3}{2}$ Heisenberg model, (b) 3-sublattice state named UUD with 1/3 magnetization and (c) TL-liquid of massless chirality with 1/3 magnetization plateau, (d) TL-liquid of massless spin mode with or without chirality quasi long-range order

Quantum Hall Systems Studied by the Density Matrix Renormalization Group Method

The ground-state and low-energy excitations of quantum Hall systems are studied by the density matrix renormalization group (DMRG) method. From the ground-state pair correlation functions and low-energy excitions, the ground-state phase diagram is determined, which consists of incompressible liquid states, Fermi liquid type compressible liquid states, and many kinds of CDW states called stripe, bubble and Wigner crystal. The spin transition and the domain formation are studied at v=2/3. The evolution from composite fermion liquid state to an excitonic state in bilayer systems is investigated at total filling factor v=1.Comment: 21 pages, 18 figure

SU(4) spin-orbit critical state in one dimension

Effect of quantum fluctuations concerned with the orbital degrees of freedom is discussed for the model with SU(4) symmetry in one dimension. An effective Hamiltonian is derived from the orbitally degenerate Hubbard model at quarter filling. This model is equivalent to the Bethe soluble SU(4) exchange model. Quantum numbers of the ground state and the lowest branch of excitations are determined. The spin-spin correlation functions are obtained numerically by the density matrix renormalization group method. It shows a power-law decay with oscillations of the period of four sites. The period originates from the interference between the spin and orbital degrees of freedom. The exponent of the power-law decay estimated from the finite size data is consistent with the prediction by the conformal field theory.Comment: 5 pages, 5 figures, REVTeX, to appear in Phys. Rev.

Kondo hole in one-dimensional Kondo insulators

Properties of a nonmagnetic impurity in Kondo insulators are investigated by considering a one-dimensional Kondo lattice model with depletion of a localized spin. The ground-state phase diagram determined by the Lanczos method shows that the magnetic moment is more stable than in ordinary metals. Temperature dependence of impurity susceptibilities is also studied by using the finite-temperature density-matrix renormalization group.Comment: 5 pages, 6 figure

Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet

Quantum spin-1/2 kagome Heisenberg antiferromagnet is the representative frustrated system possibly hosting a spin liquid. Clarifying the nature of this elusive topological phase is a key challenge in condensed matter, however, even identifying it still remains unsettled. Here, we apply a magnetic field and discover a series of spin gapped phases appearing at five different fractions of magnetization by means of grand canonical density matrix renormalization group, an unbiased state-of-art numerical technique. The magnetic field dopes magnons and first gives rise to a possible Z3 spin liquid plateau at 1/9-magnetization. Higher field induces a self-organized super-lattice-unit, a six-membered ring of quantum spins, resembling an atomic orbital structure. Putting magnons into this unit one by one yields three quantum solid plateaus. We thus find that the magnetic field could control the transition between various emergent phases by continuously releasing the frustration.Comment: 6 pages 4 figures and 4 page supplementary file. Nature Communications, accepted, July 10, 201

Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"

We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the relativistic quantum Hall states with the use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to the relativistic quantum Hall states are investigated in detail. The mass term acts as an interpolating parameter between the relativistic and non-relativistic quantum Hall effects. It is pointed out that the mass term unevenly affects the many-body physics of the positive and negative Landau levels as a manifestation of the "parity anomaly". In particular, we explicitly demonstrate the instability of the Laughlin state of the positive first relativistic Landau level with the reduction of the charge gap.Comment: We have corrected the typographic errors in our article. There are three corrections: (1)2g -> 2j in Fig.3 (2)2g -> 2j in the caption of Fig.3 (3)2g=12 -> 2j = 64 in the caption of Fig.