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Han-Dong Chen

Publications and source records attributed to Han-Dong Chen.

18 recordsLinked to original sources
arXiv2009

Probing Kitaev Models on Small Lattices

We address the following important question: how to distinguish Kitaev models experimentally realized on small lattices from other non-topological interacting spin models. Based on symmetry arguments and exact diagonalization, we show that a particularly characteristic pattern of spin-spin correlations survives despite finite size, open boundary and thermal effects. The pattern is robust against small residual perturbing interactions and can be utilized to distinguish the Kitaev interactions from other interactions such as antiferromagnetic Heisenberg interactions. The effect of external magnetic field is also considered and found to be not critical.

cond-mat.str-el↗
arXiv2009

Quantum phase diagram of fermion mixtures with population imbalance in one-dimensional optical lattices

With a recently developed time evolving block decimation (TEBD) algorithm, we numerically study the ground state quantum phase diagram of fermi mixtures with attractive inter-species interactions loaded in one-dimensional optical lattices. For our study, we adopt a general asymmetric Hubbard model (AHM) with species-dependent tunneling rates to incorporate the possibility of mass imbalance in the mixtures. We find clear signatures for the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in this model in the presence of population imbalance. Our simulation also reveals that in the presence of mass imbalance, the parameter space for FFLO states shrinks or even completely vanishes depending on the strength of the attractive interaction and the degree of mass imbalance.

quant-ph↗
arXiv2008

Complementary Pair Density Wave and d-wave Checkerboard Order in High Temperature Superconductors

The competing orders in the particle-particle (P-P) channel and the particle-hole (P-H) channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-deGennes equation self-consistently, we show that there is a general complementary connection between the d-wave checkerboard order (DWCB) in the particle-hole (P-H) channel and the pair density wave order (PDW) in the particle-particle (P-P) channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or globally through phase fluctuation should induce both orders in underdoped cuprates. The presence of both DWCB and PDW orders with $4a \times 4a$ periodicity can explain the checkerboard modulation observed in FT-STS from STM and the puzzling dichotomy between the nodal and antinodal regions as well as the characteristic features such as non-dispersive Fermi arc in the pseudogap state.

cond-mat.supr-con↗
arXiv2008

Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations

In this work, we illustrate how a Jordan-Wigner transformation combined with symmetry considerations enables a direct solution of Kitaev's model on the honeycomb lattice. We (i) express the p-wave type fermionic ground states of this system in terms of the original spins, (ii) adduce that symmetry alone dictates the existence of string and planar brane type correlators and their composites, (iii) compute the value of such non-local correlators by employing the Jordan-Wigner transformation, (iv) affirm that the spectrum is inconsequential to the existence of topological quantum order and that such information is encoded in the states themselves, and (v) express the anyonic character of the excitations in this system and the local symmetries that it harbors in terms of fermions.

cond-mat.stat-mech↗
arXiv2007

d+id'-wave Superconducting States in Graphene

We show that effective superconducting orders generally emerge at low energy in the superconducting state of graphene with conventionally defined pairing symmetry . We study such a particular interesting example, the $d_{x^2-y^2}+id'_{xy}$ spin singlet pairing superconducting state in graphene, which can be generated by electronic correlation as well as induced through a proximity effect with a d-wave superconductor. We find that effectively the d-wave state is a state with mixed s-wave and exotic $p+ip$-wave pairing orders at low energy. This remarkable property leads to distinctive superconducting gap functions and novel behavior of the Andreev conductance spectra.

cond-mat.mes-hall↗
arXiv2007

Majorana Fermions, Exact Mappings between Classical and Topological Orders

Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with topological orders can be constructed from certain well-known models with classical orders characterized by symmetry-breaking. Topology-dependent ground state degeneracy, vanishing two-point correlation functions, and unpaired Majorana fermions on boundaries emerge naturally from such construction. The approach opens a new way to construct and characterize topological orders.

cond-mat.str-el↗
arXiv2007

d-Wave Checkerboard Order in Cuprates

We show that the d-wave ordering in particle-hole channels, dubbed d-wave checkerboard order, possesses important physics that can sufficiently explain the scanning tunneling microscopy (STM) results in cuprates. A weak d-wave checkerboard order can effectively suppress the coherence peak in the single-particle spectrum while leaving the spectrum along the nodal direction almost unaffected. Simultaneously, it generates a Fermi arc with little dispersion around the nodal points at finite temperature that is consistent with the results of angle-resolved photoemission spectroscopy (ARPES) experiments in the pseudogap phase. We also show that there is a general complementary connection between the d-wave checkerboard order and the pair-density-wave order. Suppressing superconductivity locally or globally through phase fluctuations should induce both orders in underdoped cuprates and explain the nodal-antinodal dichotomy observed in ARPES and STM experiments.

cond-mat.supr-con↗
arXiv2007

Two-Point Entanglement Near a Quantum Phase Transition

In this work, we study the two-point entanglement S(i,j), which measures the entanglement between two separated degrees of freedom (ij) and the rest of system, near a quantum phase transition. Away from the critical point, S(i,j) saturates with a characteristic length scale $ξ_E$, as the distance |i-j| increases. The entanglement length $ξ_E$ agrees with the correlation length. The universality and finite size scaling of entanglement are demonstrated in a class of exactly solvable one dimensional spin model. By connecting the two-point entanglement to correlation functions in the long range limit, we argue that the prediction power of a two-point entanglement is universal as long as the two involved points are separated far enough.

cond-mat.stat-mech↗
arXiv2006

Nature of the Quantum Phase Transition in Quantum Compass Model

In this work, we show that the quantum compass model on an square lattice can be mapped to a fermionic model with local density interaction. We introduce a mean-field approximation where the most important fluctuations, those perpendicular to the ordering direction, are taken into account exactly. It is found that the quantum phase transition point at $J_x=J_z$ marks a first order phase transition. We also show that the mean field result is robust against the remaining fluctuation corrections up to the second order.

cond-mat.str-el↗
arXiv2006

Band Collapse and the Quantum Hall Effect in Graphene

The recent Quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice, and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a phenomenon which we call band collapse. As a corollary, for low magnetic field, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the "relativistic" Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.

cond-mat.mes-hall↗
arXiv2004

Magic Doping Fractions in High-Temperature Superconductors

We report hole-doping dependence of the in-plane resistivity ρ_{ab} in a cuprate superconductor La_{2-x}Sr_{x}CuO_{4}, carefully examined using a series of high-quality single crystals. Our detailed measurements find a tendency towards charge ordering at particular rational hole doping fractions of 1/16, 3/32, 1/8, and 3/16. This observation appears to suggest a specific form of charge order and is most consistent with the recent theoretical prediction of the checkerboard-type ordering of the Cooper pairs at rational doping fractions x = (2m+1)/2^n, with integers m and n.

cond-mat.supr-con↗
arXiv2004

Pair Density Wave in the Pseudogap State of High Temperature Superconductors

Recent scanning tunneling microscopy (STM) experiments of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ have shown evidence of real-space organization of electronic states at low energies in the pseudogap state. We argue based on symmetry considerations as well as model calculations that the experimentally observed modulations are due to a density wave of d-wave Cooper-pairs without global phase coherence. We show that STM measurements can distinguish a pair-density-wave from more typical electronic modulations such as those due to charge density wave ordering or scattering from an onsite periodic potential.

cond-mat.supr-con↗
arXiv2004

Global Phase Diagram of the High Tc Cuprates

The high Tc cuprates have a complex phase diagram with many competing phases. We propose a bosonic effective quantum Hamiltonian based on the projected SO(5) model with extended interactions, which can be derived from the microscopic models of the cuprates. The global phase diagram of this model is obtained using mean-field theory and the Quantum Monte Carlo simulation, which is possible because of the absence of the minus sign problem. We show that this single quantum model can account for most salient features observed in the high Tc cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. Experimental consequences are discussed and new theoretical predictions are presented.

cond-mat.supr-con↗
arXiv2004

Geometry of the 3-Qubit State, Entanglement and Division Algebras

We present a generalization to 3-qubits of the standard Bloch sphere representation for a single qubit and of the 7-dimensional sphere representation for 2 qubits presented in Mosseri {\it et al.}\cite{Mosseri2001}. The Hilbert space of the 3-qubit system is the 15-dimensional sphere $S^{15}$, which allows for a natural (last) Hopf fibration with $S^8$ as base and $S^7$ as fiber. A striking feature is, as in the case of 1 and 2 qubits, that the map is entanglement sensitive, and the two distinct ways of un-entangling 3 qubits are naturally related to the Hopf map. We define a quantity that measures the degree of entanglement of the 3-qubit state. Conjectures on the possibility to generalize the construction for higher qubit states are also discussed.

quant-ph↗
arXiv2004

Quantitative Test of SO(5) Symmetry in the Vortex State of $Nd_{1.85}Ce_{0.15}CuO_4$

By numerically solving models with competing superconducting and antiferromagnetic orders, we study the magnetic field dependence of the antiferromagnetic moment in both the weak and strong field regimes. Through a omparison with the neutron scattering results of Kang et al and Matsuura et al.on $Nd_{1.85}Ce_{0.15}CuO_4$, we conclude that this system is close to a SO(5) symmetric critical point. We also make a quantitative prediction on increasing the upper critical field $B_{c2}$ and the superconducting transition temperature $T_c$ by applying an in-plane magnetic field.

cond-mat.supr-con↗
arXiv2004

Non-abelian Berry's phase and Chern numbers in higher spin pairing condensates

We show that the non-Abelian Berry phase emerges naturally in the s-wave and spin quintet pairing channel of spin-3/2 fermions. The topological structure of this pairing condensate is characterized by the second Chern number. This topological structure can be realized in ultra-cold atomic systems and in solid state systems with at least two Kramers doublets.

cond-mat.supr-con↗