arXiv subjects

Pochung Chen

Publications and source records attributed to Pochung Chen.

At least 37 records · Page 2Linked to original sources

arXiv2015

Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry

We study the quantum critical phase of a SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the entanglement entropy and finite-size energies by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectrum, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)$_1$ Wess-Zumino-Witten model. We find that while in the whole critical phase the Hamiltonian is only SU(2) invariant, there is an emergent SU(3) symmetry in the thermodynamic limit.

cond-mat.str-el↗

arXiv2014

Quantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization

We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensions for the Kane-Fisher fixed points by modeling the single impurity as a junction (weak link) of two interacting wires. We show that the universal behavior of the junction can be easily identified within the MERA and argue that the boundary MERA framework has tremendous potential to classify the fixed points in general multi-wire junctions.

cond-mat.str-el↗

arXiv2014

Long-time dynamics of quantum chains: transfer-matrix renormalization group and entanglement of the maximal eigenvector

By using a different quantum-to-classical mapping from the Trotter-Suzuki decomposition, we identify the entanglement structure of the maximal eigenvectors for the associated quantum transfer matrix. This observation provides a deeper insight into the problem of linear growth of the entanglement entropy in time evolution using conventional methods. Based on this observation, we propose a general method for arbitrary temperatures using the biorthonormal transfer-matrix renormalization group. Our method exhibits a competitive accuracy with a much cheaper computational cost in comparison with two recent proposed methods for long-time dynamics based on a folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] and a modified time-dependent density-matrix renormalization group [Phys. Rev. Lett. 108, 227206 (2012)].

cond-mat.str-el↗

arXiv2014

A Memory of Majorana Fermions through Quantum Quench

We study the sudden quench of a one-dimensional p-wave superconductor through its topological signature in the entanglement spectrum. The long-time evolution of the system and its topological characterization depend on a pseudomagnetic field ${\bs R}_{\mbox{\text eff}}(k)$, which connects both the initial and the final Hamiltonians, hence exhibiting a memory effect. In particular, we explore the robustness of the Majorana zero-mode associated with the entanglement cut in the topologically nontrivial phase and identify the parameter space in which the mode can survive in the infinite-time limit.

cond-mat.mes-hall↗

arXiv2013

Entanglement negativity via replica trick: a Quantum Monte Carlo approach

Motivated by recent developments in conformal field theory (CFT), we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct scale invariant combinations that are related to the negativity, a true measure of entanglement for two intervals embedded in a chain. These quantities can serve as witnesses of criticality. In particular, we study several scale invariant combinations of the moments for the 1D hard-core boson model. For two adjacent intervals unusual finite size corrections are present, showing parity effects that oscillate with a filling dependent period. These are more pronounced in the presence of boundaries. For large chains we find perfect agreement with CFT. Oppositely, for disjoint intervals corrections are more severe and CFT is recovered only asymptotically. Furthermore, we provide evidence that their exponent is the same as that governing the corrections of the mutual information. Additionally we study the 1D Bose-Hubbard model in the superfluid phase. Remarkably, the finite-size effects are smaller and QMC data are already in impressive agreement with CFT at moderate large sizes.

cond-mat.str-el↗

arXiv2013

Entanglement entropy scaling of the XXZ chain

We study the entanglement entropy scaling of the XXZ chain. While in the critical XY phase of the XXZ chain the entanglement entropy scales logarithmically with a coefficient that is determined by the associated conformal field theory, at the ferromagnetic point, however, the system is not conformally invariant yet the entanglement entropy still scales logarithmically albeit with a different coefficient. We investigate how such an nontrivial scaling at the ferromagnetic point influences the estimation of the central charge $c$ in the critical XY phase. In particular we use the entanglement scaling of the finite or infinite system, as well as the finite-size scaling of the ground state energy to estimate the value of $c$. In addition, the spin-wave velocity and the scaling dimension are also estimated. We show that in all methods the evaluations are influenced by the nearby ferromagnetic point and result in crossover behavior. Finally we discuss how to determine whether the central charge estimation is strongly influenced by the crossover behavior and how to properly evaluate the central charge.

cond-mat.str-el↗

arXiv2013

Entanglement Spectroscopy using Quantum Monte Carlo

We present a numerical scheme to reconstruct a subset of the entanglement spectrum of quantum many body systems using quantum Monte Carlo. The approach builds on the replica trick to evaluate particle number resolved traces of the first n of powers of a reduced density matrix. From this information we reconstruct n entanglement spectrum levels using a polynomial root solver. We illustrate the power and limitations of the method by an application to the extended Bose-Hubbard model in one dimension where we are able to resolve the quasi-degeneracy of the entanglement spectrum in the Haldane-Insulator phase. In general the method is able to reconstruct the largest few eigenvalues in each symmetry sector and typically performs better when the eigenvalues are not too different.

cond-mat.quant-gas↗

arXiv2012

Quantum and Thermal Transitions Out of the Pair-Supersolid Phase of Two-Species Bosons in Lattice

We investigate two-species bosons in a two-dimensional square lattice by quantum Monte Carlo method. We show that the inter-species attraction and nearest-neighbor intra-species repulsion results in the pair-supersolid phase, where a diagonal solid order coexists with an off-diagonal pair-superfluid order. The quantum and thermal transitions out of the pair-supersolid phase are characterized. It is found that there is a direct first order transition from the pair-supersolid phase to the double-superfluid phase without an intermediate region. Furthermore, the melting of the pair-supersolid occurs in two steps. Upon heating, first the pair-superfluid is destroyed via a KT transition then the solid order melts via an Ising transition

cond-mat.quant-gas↗

arXiv2012

Quench Dynamics of Topological Maximally-Entangled States

We investigate the quench dynamics of the one-particle entanglement spectra (OPES) for systems with topologically nontrivial phases. By using dimerized chains as an example, it is demonstrated that the evolution of OPES for the quenched bi-partite systems is governed by an effective Hamiltonian which is characterized by a pseudo spin in a time-dependent pseudo magnetic field $\vec{S}(k,t)$. The existence and evolution of the topological maximally-entangled edge states are determined by the winding number of $\vec{S}(k,t)$ in the $k$-space. In particular, the maximally-entangled edge states survive only if nontrivial Berry phases are induced by the winding of $\vec{S}(k,t)$. In the infinite time limit the equilibrium OPES can be determined by an effective time-independent pseudo magnetic field $\vec{S}_{\mb{eff}}(k)$. Furthermore, when maximally-entangled edge states are unstable, they are destroyed by quasiparticles within a characteristic timescale in proportional to the system size.

cond-mat.str-el↗

arXiv2012

Accurate computation of low-temperature thermodynamics for quantum spin chains

We apply the biorthonormal transfer-matrix renormalization group (BTMRG) [Phys. Rev. E 83, 036702 (2011)] to study low-temperature properties of quantum spin chains. Simulation on isotropic Heisenberg spin-1/2 chain demonstrates that the BTMRG outperforms the conventional transfer-matrix renormalization group (TMRG) by successfully accessing far lower temperature unreachable by conventional TMRG, while retaining the same level of accuracy. The power of the method is further illustrated by the calculation of the low-temperature specific heat for a frustrated spin chain.

cond-mat.str-el↗

arXiv2011

Dimerized and trimerized phases for spin-2 Bosons in a one-dimensional optical lattice

We study the phase diagram for spin-2 bosons loaded in a one-dimensional optical lattice. By using non-Abelian density matrix renormalization group (DMRG) method we identify three possible phases: ferromagnetic, dimerized, and trimerized phases. We sketch the phase boundaries based on DMRG. We illustrate two methods for identifying the phases. The first method is based on the spin-spin correlation function while in the second method one observes the excitation gap as a dimerization or a trimerization superlattice is imposed. The advantage of the second method is that it can also be easily implemented in experiments. By using the scattering lengths in the literature we estimate that $^{83}$Rb, $^{23}$Na, and $^{87}$Rb be ferromagnetic, dimerized, and trimerized respectively.

cond-mat.quant-gas↗

arXiv2011

Edge State, Entanglement Entropy Spectra and Critical Hopping Coupling of Anisotropic Honeycomb Lattice

For a bipartite honeycomb lattice, we show that the Berry phase depends not only on the shape of the system but also on the hopping couplings. Using the entanglement entropy spectra obtained by diagonalizing the block Green's function matrices, the maximal entangled state with the eigenvalue $λ_m=1/2$ of the reduced density matrix is shown to have one-to-one correspondence to the zero energy states of the lattice with open boundaries, which depends on the Berry phase. For the systems with finite bearded edges along $x$-direction we find critical hopping couplings: the maximal entangled states (zero-energy states) appear pair by pair if one increases the hopping coupling $h$ over the critical couplings $h_c$s.

cond-mat.other↗

arXiv2010

Dynamical Decoupling of Qubits in Spin Bath under Periodic Quantum Control

We investigate the feasibility for the preservation of coherence and entanglement of one and two spin qubits coupled to an interacting quantum spin-1/2 chain within the dynamical decoupling (DD) scheme. The performance is examined by counting number of computing pulses that can be applied periodically with period of $T$ before qubits become decoherent, while identical decoupling pulse sequence is applied within each cycle. By considering pulses with mixed directions and finite width controlled by magnetic fields, it is shown that pulse-width accumulation degrades the performance of sequences with larger number of pulses and feasible magnetic fields in practice restrict the consideration to sequences with number of decoupling pulses being less than 10 within each cycle. Furthermore, within each cycle $T$, exact nontrivial pulse sequences are found for the first time to suppress the qubit-bath coupling to $O(T^{N+1})$ progressively with minimum number of pulses being $4,7,12$ for $N=1,2,3$. These sequences, when applied to all qubits, are shown to preserve both the entanglement and coherence. Based on time-dependent density matrix renormalization, our numerical results show that for modest magnetic fields (10-40 Tesla) available in laboratories, the overall performance is optimized when number of pulses in each cycle is 4 or 7 with pulse directions be alternating between x and z. Our results provide useful guides for the preservation of coherence and entanglement of spin qubits in solid state.

quant-ph↗

arXiv2010

Quantum Criticality from in-situ Density Imaging

We perform large-scale Quantum Monte Carlo (QMC) simulations for strongly interacting bosons in a 2D optical lattice trap, and confirm an excellent agreement with the benchmarking in-situ density measurements by the Chicago group [1]. We further present a general finite temperature phase diagram both for the uniform and the trapped systems, and demonstrate how the universal scaling properties near the superfluid(SF)-to-Mott insulator(MI) transition can be observed by analysing the in-situ density profile. The characteristic temperature to find such quantum criticality is estimated to be of the order of the single-particle bandwidth, which should be achievable in the present or near future experiments. Finally, we examine the validity regime of the local fluctuation-dissipation theorem (FDT), which can be a used as a thermometry in the strongly interacting regime.

cond-mat.quant-gas↗

arXiv2010

Quantum phase transitions of two-species bosons in square lattice

We investigate various quantum phase transitions of attractive two-species bosons in a square lattice. Using the algorithm based on the tensor product states, the phase boundaries of the pair superfluid states with nonzero pair condensate density \emph{and} vanishing atomic condensate density are determined. Various quantum phase transitions across the phase boundaries are characterized. Our work thus provides guides to the experimental search of the pair superfluid phase in lattice boson systems.

cond-mat.str-el↗

arXiv2010

Field Induced Spin Supersolidity in Frustrated Spin-1/2 Spin-Dimer Models

By means of the recently developed algorithm based on the tensor product states, the magnetization process of frustrated spin-1/2 spin-dimer models on a square lattice is investigated. Various field-induced quantum phases are discovered. In particular, clear evidence of a supersolid phase over a finite regime of magnetic field is observed. Critical fields at various field-induced transitions are determined accurately. Our work not only implies that the employed numerical technique can be an efficient algorithm even for the frustrated spin systems, but also shed light on the search of the supersolid phase in real frustrated spin-dimer compounds.

cond-mat.str-el↗

arXiv2009

Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States

By means of the recently proposed algorithm based on the tensor product states, the magnetization process of the spin-1/2 anti-ferromagnetic XXZ model on a square lattice is investigated. In the large spin-anisotropy limit, clear evidence of a first-order spin-flip transition is observed as an external magnetic field is increased. Our findings of the critical field and the discrete jumps in various local order parameters are in good agreement with the quantum Monte Carlo data in the literature. Our results imply that this algorithm can be an accurate and efficient numerical approach in studying first-order quantum phase transitions in two dimensions.

cond-mat.str-el↗

arXiv2009

Interaction-induced first order correlation between spatially-separated 1D dipolar fermions

We calculate the ground-state properties of fermionic dipolar atoms or molecules in a one-dimensional double-tube potential by using the Luttinger liquid theory and the density matrix renormalization-group calculation. When the external field is applied near a magic angle with respect to the double-tube plane, the long-ranged dipolar interaction can generate a spontaneous correlation between fermions in different tubes, even when the bare intertube tunneling rate is negligibly small. Such interaction-induced correlation strongly enhances the contrast of the interference fringes and therefore can be easily observed in the standard time-of-flight experiment.

cond-mat.str-el↗