Dynamical Mean Field Theory of the Gutzwiller-projected BCS Hamiltonian: Phase Fluctuations and the Pseudogap

One of the most prominent problems in high temperature superconductivity is the nature of the pseudogap phase in underdoped regimes; particularly important is the role of phase fluctuations. The Gutzwiller-projected BCS Hamiltonian is a useful model for high temperature superconductivity due to an exact mapping to the Heisenberg model at half filling and generally a very close connection to the t-J model at moderate doping. We develop the dynamical mean field theory for the d-wave BCS Hamiltonian with on-site repulsive interaction, $U$, physically imposing the partial Gutzwiller projection. For results, two pseudogap energy scales are identified: one associated with the bare pairing gap for the singlet formation and the other with the local phase coherence. The real superconducting gap determined from sharp coherence peaks in the density of states shows strong renormalization from the bare value due to $U$.Comment: 8 pages, 5 figure

A Passage to Topological Matter: Colloquium

Topological matter has become one of the most important subjects in contemporary condensed matter physics. Here, I would like to provide a pedagogical review explaining some of the main ideas, which were pivotal in establishing topological matter as such an important subject. Specifically, I explain how the integer quantum Hall state played the role as a prototype for topological insulator, eventually leading to the concept of topological matter in general. The topological nature of the integer quantum Hall state is best represented by the Thouless-Kohmoto-Nightingale-den Nijs, or so-called TKNN formula, which connects between the Berry phase and the Hall conductivity. The topological non-triviality of topological insulator stems from the existence of a Dirac monopole in an appropriate, but often hidden Hamiltonian parameter space. Interestingly, having the identical Dirac monopole structure, the Hamiltonian describing the Rabi oscillation bears the essence of topological insulator. The concept of topological matter has expanded to include topological semimetals such as Weyl and Dirac semimetals. A final frontier in the research of topological matter is the interaction-induced topological phases of matter, namely, the fractional Chern and topological insulators. The existence of the fractional Chern and topological insulators has been proposed theoretically by drawing an analogy from the fractional quantum Hall states. The gist of this proposal is explained along with some of its issues. I conclude this review by discussing some of the future directions in the research of topological matter.Comment: 16 pages, 8 figure

Theory of Tunneling in the Exciton Condensate of Bilayer Quantum Hall Systems

We develop a theory of interlayer tunneling in the exciton condensate of bilayer quantum Hall systems, which predicts strongly enhanced, but finite, tunneling conductance peaks near zero bias even at zero temperature. It is emphasized that, though this strongly enhanced tunneling originates from spontaneous interlayer phase coherence, it is fundamentally not the Josephson effect. Because of strong interlayer correlation, the bilayer system behaves as a single system so that conventional tunneling theories treating two layers as independent systems are not applicable. Based on our theory, we compute the height of conductance peak as a function of interlayer distance, which is in good agreement with experiment.Comment: 5 pages, 5 figure

Ground states of quantum antiferromagnets in two dimensions

We explore the ground states and quantum phase transitions of two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and Jalabert (Mod. Phys. Lett. B 4, 1043 (1990), http://onsager.physics.yale.edu/p32.pdf). The `minimal' model for square lattice antiferromagnets is a lattice discretization of the quantum non-linear sigma model, along with Berry phases which impose quantization of spin. With full SU(2) spin rotation invariance, we find a magnetically ordered ground state with Neel order at weak coupling, and a confining paramagnetic ground state with bond charge (e.g. spin Peierls) order at strong coupling. We study the mechanisms by which these two states are connected in intermediate coupling. We extend the minimal model to study different routes to fractionalization and deconfinement in the ground state, and also generalize it to cases with a uniaxial anisotropy (the spin symmetry group is then U(1)). For the latter systems, fractionalization can appear by the pairing of vortices in the staggered spin order in the easy-plane; however, we argue that this route does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant systems we study a separate route to fractionalization associated with the Higgs phase of a complex boson measuring non-collinear, spiral spin correlations: we present phase diagrams displaying competition between magnetic order, bond charge order, and fractionalization, and discuss the nature of the quantum transitions between the various states. A strong check on our methods is provided by their application to S=1/2 frustrated antiferromagnets in one dimension: here, our results are in complete accord with those obtained by bosonization and by the solution of integrable models.Comment: 44 pages, 19 figures; SS web page: http://pantheon.yale.edu/~subir (v2) updated discussion of literatur

Distributed Topology Design for Network Coding Deployed Large-scale Sensor Networks

In this paper, we propose a solution to the distributed topology formation problem for large-scale sensor networks with multi-source multicast flows. The proposed solution is based on game-theoretic approaches in conjunction with network coding. The proposed algorithm requires significantly low computational complexity, while it is known as NP-hard to find an optimal topology for network coding deployed multi-source multicast flows. In particular, we formulate the problem of distributed network topology formation as a network formation game by considering the nodes in the network as players that can take actions for making outgoing links. The proposed solution decomposes the original game that consists of multiple players and multicast flows into independent link formation games played by only two players with a unicast flow. We also show that the proposed algorithm is guaranteed to determine at least one stable topology. Our simulation results confirm that the computational complexity of the proposed solution is low enough for practical deployment in large-scale networks

Two-species branching annihilating random walks with one offspring

We study the effects of hard core (HC) interactions between different species of particles on two-species branching annihilating random walks with one offspring(BAW$_2$(1)). The single-species model belongs to the directed percolation (DP) universality class. In the BAW$_2$(1) model, a particle creates one particle of the same species in its neighborhood with the probability $\sigma (1-p)$ and of the different species with $(1-\sigma)(1-p)$, where $p$ is the hopping probability. Without HC interactions, this model always exhibits the DP-type absorbing transition for all $\sigma$. Even with HC interactions, the nature of the phase transitions does not change except near $\sigma=0$, where the HC interaction destabilizes and completely wipes away the absorbing phase. The model is always active except at the annihilation fixed point of zero branching rate ($p=1$). Critical behavior near the annihilation fixed point is characterized by exponents $\beta = \nu_\perp =1/2$ and $\nu_{||} = 1$.Comment: 4 pages, APCTP international workshop on similarity in diversity (Seoul, Korea; Aug.24, 2000): To appear in Journal of the Korean Physical Societ

Floquet Topological Semimetal with Nodal Helix

Topological semimetals with nodal line are a novel class of topological matter extending the concept of topological matter beyond topological insulators and Weyl/Dirac semimetals. Here, we show that a Floquet topological semimetal with nodal helix can be generated by irradiating graphene or the surface of a topological insulator with circularly polarized light. Nodal helix is a form of nodal line running across the Brillouin zone with helical winding. Specifically, it is shown that the dynamics of irradiated graphene is described by the time Stark Hamiltonian, which can host a Floquet topological insulator and a weakly driven Floquet topological semimetal with nodal helix in the high and low frequency limits, respectively. It is predicted that, at low frequency, the $\pi$ shift of the Zak phase generates a topological discontinuity along the projected nodal helix in the momentum spectrum of the Floquet states. At intermediate frequency, this topological discontinuity can create an interesting change of patterns in the quasienergy dispersion of the Floquet states.Comment: 11 pages, 5 figure

Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator

Motivated by the close analogy with the fractional quantum Hall states (FQHSs), fractional Chern insulators (FCIs) are envisioned as strongly correlated, incompressible states emerging in a fractionally filled, (nearly) flat band with non-trivial Chern number. Built upon this vision, fractional topological insulators (FTIs) have been proposed as being composed of two independent copies of the FCI with opposite Chern numbers for different spins, preserving the time-reversal symmetry as a whole. An important question is if the correlation between electrons with different spins can be really ignored. To address this question, we investigate the effects of correlation in the presence of spin-dependent holomorphicity, i.e., electrons of one spin species reside in the holomorphic lowest Landau level, while those of the other in the antiholomorphic counterpart. By constructing and performing exact diagonalization of an appropriate model Hamiltonian, here, we show that generic, strongly correlated, fractionally filled states with spin-dependent holomorphicity cannot be described as two independent copies of the FQHS, suggesting that FTIs in the lattice cannot be described as those of the FCI either. Fractionally filled states in this system are generally compressible except at half filling, where an insulating state called the half-filled spin-holomorphic FTI occurs. It is predicted that the half-filled spin-holomorphic FTI is susceptible to an inherent spontaneous symmetry breaking, leading to the spatial separation of spins.Comment: 9 pages and 5 figure

Network Coding Based Evolutionary Network Formation for Dynamic Wireless Networks

In this paper, we aim to find a robust network formation strategy that can adaptively evolve the network topology against network dynamics in a distributed manner. We consider a network coding deployed wireless ad hoc network where source nodes are connected to terminal nodes with the help of intermediate nodes. We show that mixing operations in network coding can induce packet anonymity that allows the inter-connections in a network to be decoupled. This enables each intermediate node to consider complex network inter-connections as a node-environment interaction such that the Markov decision process (MDP) can be employed at each intermediate node. The optimal policy that can be obtained by solving the MDP provides each node with optimal amount of changes in transmission range given network dynamics (e.g., the number of nodes in the range and channel condition). Hence, the network can be adaptively and optimally evolved by responding to the network dynamics. The proposed strategy is used to maximize long-term utility, which is achieved by considering both current network conditions and future network dynamics. We define the utility of an action to include network throughput gain and the cost of transmission power. We show that the resulting network of the proposed strategy eventually converges to stationary networks, which maintain the states of the nodes. Moreover, we propose to determine initial transmission ranges and initial network topology that can expedite the convergence of the proposed algorithm. Our simulation results confirm that the proposed strategy builds a network which adaptively changes its topology in the presence of network dynamics. Moreover, the proposed strategy outperforms existing strategies in terms of system goodput and successful connectivity ratio.Comment: IEEE Transactions on Mobile Computing (Early Access

Towards Interactive Object-Oriented Programming

To represent interactive objects, we propose a choice-disjunctive declaration statement of the form S R where S;R are the (procedure or field) declaration statements within a class. This statement has the following semantics: request the user to choose one between S and R when an object of this class is created. This statement is useful for representing interactive objects that require interactions with the user