arXiv subjects

T. Xiang

Publications and source records attributed to T. Xiang.

At least 37 records · Page 2Linked to original sources

arXiv2016

Heisenberg antiferromagnet on the Husimi lattice

We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on Projected Entangled Simplex States (PESS). The nature of the ground state varies strongly with the spin quantum number, $S$. For $S = 1/2$, it is an algebraic (gapless) quantum spin liquid. For $S = 1$, it is a gapped, non-magnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For $S = 2$, it is a simplex-solid state with a spin gap and no symmetry-breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For $S = 3/2$, and indeed for all spin values $S \ge 5/2$, the ground states have $120$-degree antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of $S$, there is always a plateau in the magnetization at $m = 1/3$.

cond-mat.str-el↗

arXiv2015

Probing the Hofstadter butterfly with the quantum oscillation of magnetization

We have developed a different quantum transfer matrix method to accurately determine thermodynamic properties of the Hofstadter model. This method resolves a technical problem which is intractable by other methods and makes the calculation of physical quantities of the Hofstadter model in the thermodynamic limit at finite temperatures feasible. It is shown that the quantum correction to the de Haas-van Alphen (dHvA) oscillation of magnetization bears the energy structure of Hofstadter butterfly. The measurement of this quantum correction, which can be materialized on the superlattice or cold atom systems, can reveal unambiguously the Hofstadter fractal energy spectrum.

cond-mat.str-el↗

arXiv2014

Progress towards quantum simulating the classical O(2) model

We connect explicitly the classical $O(2)$ model in 1+1 dimensions, a model sharing important features with $U(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization group formulation, we take the time continuum limit and check that finite dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}$Rb and $^{41}$K Bose-Bose mixture.

hep-lat↗

arXiv2014

Partial long-range order in antiferromagnetic Potts models

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered. This situation may arise from frustration of the interactions, but also from an irregular but unfrustrated lattice structure. We study partial long-range order in a range of antiferromagnetic $q$-state Potts models on different two-dimensional lattices and for all relevant values of $q$. We exploit the power of tensor-based numerical methods to evaluate the partition function of these models and hence to extract the key thermodynamic properties -- entropy, specific heat, magnetization, and susceptibility -- giving deep insight into the phase transitions and ordered states of each system. Our calculations reveal a range of phenomena related to partial ordering, including different types of entropy-driven phase transition, the role of lattice irregularity, very large values of the critical $q_c$, and double phase transitions.

cond-mat.stat-mech↗

arXiv2014

Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice

We investigate the 2- and 3-state ferromagnetic Potts models on the simple cubic lattice using the tensor renormalization group method with higher-order singular value decomposition (HOTRG). HOTRG works in the thermodynamic limit, where we use the $Z_q$ symmetry of the model, combined with a new measure for detecting the transition, to improve the accuracy of the critical point for the 2-state model by two orders of magnitude, obtaining $T_c = 4.51152469(1)$. The 3-state model is far more complex, and we improve the overall understanding of this case by calculating its thermodynamic quantities with high accuracy. Our results verify the first-order nature of the phase transition and the HOTRG transition temperature benchmarks the most recent Monte Carlo result.

cond-mat.stat-mech↗

arXiv2014

Localized in-gap state in a single electron doped Mott insulator

Motivated by the recent atomic-scale scanning tunneling microscope (STM) observation for a spatially localized in-gap state in an electron doped Mott insulator, we evaluate the local electronic state of the Hubbard model on the square lattice using the cluster perturbation theory. An in-gap state is found to exist below the upper Hubbard band around the dopant lattice site, which is consistent with the STM measurements. The emergence of this local in-gap state is accompanied with a rapid reduction of the double occupancy of electrons. A similar in-gap state is also found to exist on the triangular lattice. These results suggest that the in-gap state is an inherent feature of Mott insulators independent of the lattice structure.

cond-mat.str-el↗

arXiv2014

Tensor renormalization of quantum many-body systems using projected entangled simplex states

We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS), for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states (PEPS) to a simplex. PESS are an exact representation of the simplex solid states and provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.

cond-mat.str-el↗

arXiv2013

Controlling sign problems in spin models using tensor renormalization

We consider the sign problem for classical spin models at complex $β=1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$β$ than the reweighting Monte Carlo method. For the Ising model with complex $β$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

hep-lat↗

arXiv2013

Tensor renormalization group study of classical XY model on the square lattice

Using the tensor renormalization group method based on the higher-order singular value decom- position, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free energy, the internal energy and the specific heat agree with the Monte Carlo calculations. From the field dependence of the magnetic susceptibility, we find the Kosterlitz-Thouless transition temperature to be 0.8921 \pm 0.0019, consistent with the Monte Carlo as well as the high temperature series expansion results. At the transition temperature, the critical exponent δis estimated as 14.5, close to the analytic value by Kosterlitz.

cond-mat.stat-mech↗

arXiv2013

Exact blocking formulas for spin and gauge models

Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local blocking formulas and exact coarse grained expressions for the partition function. We argue that similar results should hold for most models studied by lattice gauge theorists. We provide exact blocking formulas for several 2D spin models (the O(2) and O(3) sigma models and the SU(2) principal chiral model) and for the 3D gauge theories with groups Z_2, U(1) and SU(2). We briefly discuss generalizations to other groups, higher dimensions and practical implementations.

hep-lat↗

arXiv2013

Partial order in Potts models on the generalized decorated square lattice

We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) interactions. Using the tensor renormalization-group method augmented by higher-order singular value decompositions, we calculate the spontaneous magnetization of the Potts model with q = 2, 3, and 4. The results for q = 2 allow us to benchmark our numerics using the exact solution. For q = 3, we find a highly degenerate ground state with partial order on a single sublattice, but with vanishing entropy per site, and we obtain the phase diagram as a function of the ratio J2=J1. There is no finite-temperature transition for the q = 4 case when J1 = J2, but the magnetic susceptibility diverges as the temperature goes to zero, showing that the model is critical at T = 0.

cond-mat.stat-mech↗

arXiv2013

Interface-induced superconductivity and strain-dependent spin density wave in FeSe/SrTiO3 thin films

The record of superconducting transition temperature(Tc) has long been 56K for the iron-based high temperature superconductors(Fe-HTS's). Recently, in single layer FeSe films grown on SrTiO3 substrate, signs for a new 65K Tc record are reported. Here with in-situ photoemission measurements, we substantiate the presence of the spin density wave(SDW) in FeSe films, a key ingredient of Fe-HTS that was missed in FeSe before, which weakens with increased thickness or reduced strain. We demonstrate that the superconductivity occurs when the electrons transferred from the oxygen-vacant substrate suppress the otherwise most pronounced SDW in single layer FeSe. Besides providing a comprehensive understanding of FeSe films and directions to further enhance its Tc, we establish the phase diagram of FeSe vs. lattice constant that contains all the essential physics of Fe-HTS's. With the simplest structure, cleanest composition and single tuning parameter, it is ideal for testing theories of Fe-HTS's.

cond-mat.supr-con↗

arXiv2012

The Quantum Torus Chain

We introduce a new set of one dimensional quantum lattice models which we refer to as The quantum torus chain. These models have discrete global symmetry, and projective on-site representations. They possess an integer-valued parameter which controls the presence or absence of frustration. Depending on whether this parameter is even or odd these models either exhibit gapped symmetry breaking phases with isolated critical points, or gapped symmetry breaking phases separated by gapless phases. We discuss the property of these phases and phase transitions for two special values of the parameter and point out many open problems

cond-mat.str-el↗

arXiv2012

Coarse-graining renormalization by higher-order singular value decomposition

We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum lattice models in two- or three-dimensions. We have demonstrated this method using the Ising model on the square and cubic lattices. By keeping up to 16 bond basis states, we obtain by far the most accurate numerical renormalization group results for the 3D Ising model. We have also applied the method to study the ground state as well as finite temperature properties for the two-dimensional quantum transverse Ising model and obtain the results which are consistent with published data.

cond-mat.stat-mech↗

arXiv2012

Penetration depth study of LaOs$_4$Sb$_{12}$: Multiband s-wave superconductivity

We measured the magnetic penetration depth $λ(T)$ in single crystals of LaOs$_{4}$Sb$_{12}$ ($T_c$=0.74 K) down to 85 mK using a tunnel diode oscillator technique. The observed low-temperature exponential dependence indicates a s-wave gap. Fitting the low temperature data to BCS s-wave expression gives the zero temperature gap value $Δ(0)= (1.34 \pm 0.07) k_B T_c$ which is significantly smaller than the BCS value of 1.76$k_B T_c$. In addition, the normalized superfluid density $ρ(T)$ shows an unusually long suppression near $T_c$, and are best fit by a two-band s-wave model.

cond-mat.supr-con↗

arXiv2012

Two-magnon Raman scattering in A$_{0.8}$Fe$_{1.6}$Se$_2$ systems: competition between superconductivity and antiferromagnetic order

We have performed Raman-scattering measurements on high-quality single crystals of A$_{0.8}$Fe$_{1.6}$Se$_2$ superconductors of several compositions. We find a broad, asymmetric peak around 1600 cm$^{-1}$ (200 meV), which we identify as a two-magnon process involving optical magnons. The intensity of the two-magnon peak falls sharply on entering the superconducting phase. This effect, which is entirely absent in the non-superconducting system KFe$_{1.5}$Se$_2$, requires a strong mutual exclusion between antiferromagnetism and superconductivity arising from proximity effects within regions of microscale phase separation.

cond-mat.supr-con↗

arXiv2012

Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice

We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition.

cond-mat.str-el↗

arXiv2011

Partial order and finite-temperature phase transitions in Potts models on irregular lattices

We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union- Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature phase transition to a partially ordered state. From the thermodynamics of Potts models on the diced and centered diced lattices, we propose that finite-temperature transitions and partially ordered states are ubiquitous on irregular lattices.

cond-mat.str-el↗