Universal spectral form factor for many-body localization

We theoretically study correlations present deep in the spectrum of many-body-localized systems. An exact analytical expression for the spectral form factor of Poisson spectra can be obtained and is shown to agree well with numerical results on two models exhibiting many-body-localization: a disordered quantum spin chain and a phenomenological $l$-bit model based on the existence of local integrals of motion. We also identify a universal regime that is insensitive to the global density of states as well as spectral edge effects.

Eigenstate phases with finite on-site non-Abelian symmetry

We study the eigenstate phases of disordered spin chains with on-site finite non-Abelian symmetry. We develop a general formalism based on standard group theory to construct local spin Hamiltonians invariant under any on-site symmetry. We then specialize to the case of the simplest non-Abelian group, $S_3$, and numerically study a particular two parameter spin-1 Hamiltonian. We observe a thermal phase and a many-body localized phase with a spontaneous symmetry breaking (SSB) from $S_3$ to $mathbb{Z}_3$ in our model Hamiltonian. We diagnose these phases using full entanglement distributions and level statistics. We also use a spin-glass diagnostic specialized to detect spontaneous breaking of the $S_3$ symmetry down to $mathbb{Z}_3$. Our observed phases are consistent with the possibilities outlined by Potter and Vasseur [Phys. Rev. B 94, 224206 (2016)], namely thermal/ ergodic and spin-glass many-body localized (MBL) phases. We also speculate about the nature of an intermediate region between the thermal and MBL+SSB regions where full $S_3$ symmetry exists.

Computational Power of Symmetry-Protected Topological Phases

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Symmetry-protected topological phases with uniform computational power in one dimension

We investigate the usefulness of ground states of quantum spin chains with symmetry-protected topological order (SPTO) for measurement-based quantum computation. We show that, in spatial dimension one, if an SPTO phase supports quantum wire, then, subject to an additional symmetry condition that is satisfied in all cases so far investigated, it can also be used for quantum computation.

Effect of earth rotation on pair production of Standard Model Higgs bosons at linear colliders in the noncommutative space-time

We study the neutral Higgs boson pair production through $e^{+} e^{-}$ collision in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps of this to the first order of the noncommutative parameter $Theta_{mu u}$. This process is forbidden in the standard model at the tree level with background space-time being commutative. After including the effects of earths rotation we analyse the time-averaged cross section of the pair production of Higgs boson (in the light of LEP II and LHC data) at the future Linear Collider which can be quite significant for the NC scale $Lambda$ lying in the range $0.3 - 1.0$ TeV. For the 125 GeV Higgs mass(the most promising value of Higgs mass as reported by LHC), we find the NC scale as $330 rm{GeV}$ $le Lambda le 660 rm{GeV}$ and using $m_h = 129(127.5) rm{GeV}$ (the lower threshold value of the excluded region of $m_h$ reported by ATLAS(CMS) collaborations of LHC), we find the bound on $Lambda$ as: (i) $339 (336) rm{GeV} le Lambda le 677 (670) rm{GeV}$ corresponding to the Linear Collider energy $E_{com} = 500 rm{GeV}$.

Laboratory frame analysis of $e^+ e^- to mu^+ mu^-$ scattering in the Noncommutative Standard Model

We study the muon pair production $ e^+ e^- to mu^+ mu^-$ in the framework of the non-minimal noncommutative(NC) standard model to the second order of the NC parameter $Theta_{mu u}$. The $mathcal{O}(Theta^2)$ momentum dependent NC interaction significantly modifies the cross section and angular distributions which are different from the standard model. After including the effects of earths rotation we analyse the time-averaged and time dependent observables in detail. The time-averaged azimuthal distribution of the cross section shows siginificant departure from the standard model. We find strong dependence of the total cross section(time- averaged) and their distributions on the orientation of the noncommutative electric vector (${vec{Theta}}_E$). The periodic variation of the total cross-section with time over a day seems to be startling and can be thoroughly probed at the upcoming Linear Collider(LC).

Neutral Higgs boson pair production at the LC in the Noncommutative Standard Model

We study the Higgs boson pair production through $e^+e^-$ collision in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps of this to the first order of the noncommutative parameter $Theta_{mu u}$. This process is forbidden in the standard model with background space-time being commutative. We find that the cross section of the pair production of Higgs boson (of intermediate and heavy mass) at the future Linear Collider(LC) can be quite significant for the NC scale $Lambda$ lying in the range $0.5 - 1.0$ TeV. Finally, using the direct experimental(LEP II, Tevatron and global electro-weak fit) bound on Higgs mass, we obtain bounds on the NC scale as 665 GeV $le Lambda le 998$ GeV.

$e^+ e^- to mu^+ mu^-$ scattering in the Noncommutative standard model

We study muon pair production $ e^+ e^- to mu^+ mu^-$ in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps of this to the second order of the noncommutative parameter $Theta_{mu u}$. Using $mathcal{O}(Theta^2)$ Feynman rules, we find the $mathcal{O}(Theta^4)$ cross section(with all other lower order contributions simply cancelled) for the pair production. The momentum dependent $mathcal{O}(Theta^2)$ NC interaction significantly modifies the cross section and angular distributions which are different from the commuting standard model. We study the collider signatures of the space-time noncommutativity at the International Linear Collider(ILC) and find that the process $ e^+ e^- to mu^+ mu^-$ can probe the NC scale $Lambda$ in the range $0.8 - 1.0$ TeV for typical ILC energy ranges.