Quantum Matter

Electrons in conjugated organic polymers and molecules are strongly correlated since most of these systems are quasi one-dimensional.  Experimental evidences include existence of two photons below one photon state, observation of negative spin densities in polyene radicals and qualitatively different behavior of  optical gaps in polyenes and closely related symmetric cynanine dyes in the thermodynamic limiy. In this talk, I will introduce the model Hamiltonians for the electron states in conjugated systems. The DMRG method is ideally suited for their study.  Modifications to the DMRG method to obtain important low-lying states of  the systems and methods of obtaining linear and nonlinear optical response coefficients using the DMRG technique will be discussed [1-4]. Application of the method to the study of a wide variety of conjugated systems will be touched upon [5,7]. I will also discuss some recent applications of wave-packet dynamics in the study of some time-dependent phenomena [8]. References [1] S. Ramasesha, Swapan K Pati, H.R. Krishnamurthy, Z. Shuai and J. L. Br´edas, (1996) “Symmetrized DMRG method for the excited states of Hubbard models”, Phys. Rev. B 54, 7598. [2] Z. Shuai, J. L. Br´edas, Swapan K. Pati and S. Ramasesha, (1998) “Comment on the exciton binding energy in the strong correlation limit of conjugated chains”, Phys. Rev. B 58, 15329. [3] Z. Shuai, J. L. Br´edas, Swapan K. Pati and S. Ramasesha, (1997) “Quan­tum confinement effects on the ordering of the lowest-lying excited states in conjugated chains”, Phys. Rev. B 56, 9298. [4] Swapan K Pati, S. Ramasesha, Z. Shuai and J. L. Br´edas, (1999) “Dynamic nonlinear optical properties from the symmetrized density matrix renormal­ization group method”, Phys. Rev. B 59, 14827. [5] C. Raghu, Y. Anusooya Pati and S. Ramasesha, (2002) “A density matrix renormalization group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model”, Phys. Rev. B 66, 035116. [6] S. Mukhopadhyay  and  S. Ramasesha (2009) “Study of linear and nonlinear optical properties of  dendrimers using density matrix renormalization group method”,  J. Chem.  Phys.  131, 074111. [7] M. Kumar and S. Ramasesha, (2010) “A DMRG Study of the Low-Lying States of Transverse Substituted Trans-polyacetylene and Trans-polyacetylene”, Phys. Rev. B. 81, 035115 [8] Tirthankar Dutta and S. Ramasesha, (2010) “Double time window targeting technique: Real-time DMRG dynamics in Pariser-Parr-Pople model”, Phys. Rev. B 82, 035115. [9] Simil Thomas, Daniel Garcia, Karen Hallberg and S. Ramasesha "Fused Azulenes: Possible Organic Multiferroics", Phys. Rev. B RC (communicated)

Large quantum fluctuations in certain quantum spin systems destroy long range magnetic order such as antiferromagnetism. Resulting paramagnetic states are called a quantum spin liquids. These states support emergent gauge fields [1]. Under certain conditions, emergent gauge fields condense in the ground state, leading to a chiral spin liquid state [2]. A condensed `magnetic field' for example, correspond to presence of spontaneous circulating spin current or spin `chirality'[3]. In the light of recent search for spin liquids in frustrated quantum antiferromagnets, we revive our earlier approach and show that a variety of chiral spin liquid states are possible in 2D lattices.   [1] G. Baskaran and P.W. Anderson, Phys. Rev., B 37, 580 (1988) [2] V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett., 59, 2095 (1987) [3] X.-G. Wen, F. Wilczek and A. Zee, Phys. Rev., B 39, 11413 (1989) [4] G Baskaran, Phys. Rev. Lett., 63, 2524 (1989)

The ground state phase of spin-1/2 J1-J2 antiferromagnetic Heisenberg model on square lattice in the maximally frustrated regime (J2 ~ 0.5J1) has been debated for decades. Here we study this model by using a recently proposed novel numerical method - the cluster update algorithm for tensor product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with the state of art exact diagonalization study, and
the energy differences between these two studies are of the order of 0.001 J1 per site. At the largest bond dimension available D (D = 9), we find a paramagnetic ground state without any valence bond solid order in the thermodynamic limit in the range of 0.5 <= J2/J1 <= 0.6, which implies the emergence of a spin-liquid phase. Furthermore, we investigate the topologically ordered nature of such a spin-liquid phase by measuring a nonzero topological entanglement entropy.

We propose a form of parallel computing on classical computers that is based on matrix product states. The virtual parallelization is accomplished by evolving all possible results for multiple inputs, with bits represented by matrices. The action by classical probabilistic 1-bit and deterministic 2-bit gates such as NAND are implemented in terms of matrix operations and, as opposed to quantum computing, it is possible to copy bits. We present a way to explore this method of computation to solve search problems and count the number of solutions. We argue that if the classical computational cost of testing solutions (witnesses) requires less than O(n^2) local two-bit gates acting on n bits, the search problem can be fully solved in subexponential time. Therefore, for this restricted type of search problem, the virtual parallelization scheme is faster than Grover’s quantum algorithm.

As helium-4 is cooled below 2.17 K in undergoes a phase transition to a state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent advances in nanofabrication techniques allow for the construction of smooth pores with nanometer radii, that approach the truly one dimensional limit. In one dimension, it is believed that a system of bosons (like helium-4) may have startlingly different behavior than in three dimensions. The one dimensional system is predicted to have a linear hydrodynamic description known as Luttinger liquid theory, where no type of long range order can be sustained. In the limit where the pore radius is small,  helium inside the channel would behave as a sort of quasi-supersolid with all correlations decaying as power-laws at zero temperature.  We have performed large scale quantum Monte Carlo simulations of helium-4 inside nanopores of varying radii at low temperatures with realistic helium-helium and helium-pore interactions. The results indicate that helium inside the nanopore forms concentric cylindrical layers surrounding a core that can be fully described via Luttinger liquid theory and provides insights towards the exciting possibility of the experimental detection of a Luttinger liquid.