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"Mukherjee, Anirban"
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Scaling theory for Mott-Hubbard transitions: I. T = 0 phase diagram of the 1/2-filled Hubbard model
We present a T = 0 K renormalization group (RG) phase diagram for the electronic Hubbard model in two dimensions on the square lattice at half filling. The RG procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every RG step. The resulting phase diagram thus possesses the quantum fluctuation energy scale (ω) as one of its axes. A relation is derived between ω and the effective temperature scale upto which gapless, as well as emergent gapped phases can be obtained. We find that the normal and insulating phases of the half-filled Hubbard model correspond, for any on-site repulsion, to a marginal Fermi liquid normal phase and a topologically-ordered gapped Mott insulating liquid respectively. The marginal Fermi liquid is found to arise from singular forward scattering in directions normal to the nested Fermi surface, while singular backscattering events lead to Mott liquid state. The transition between these two phases involves passage through a pseudogapped phase bookended by Fermi surface topology-changing Lifshitz transitions. The pseudogap phase is observed to arise from the electronic differentiation encoded within the nested Fermi surface, and involves the gradual gapping of the Fermi surface from antinodes to nodes via charge and spin excitations that are mutually entangled. We obtain effective Hamiltonians for various phases, as well as wavefunctions for the low-energy many-body eigenstates of the Mott liquid. Benchmarking of the ground-state energy per particle and the double-occupancy fraction for the Mott liquid against existing numerical results yields excellent agreement. Presence of a Néel ordering symmetry-breaking perturbation in the RG leads to an antiferromagnetic spin-ordered charge insulating Mott state. Our results thus offer novel insights on a variety of aspects of the Mott-Hubbard problem, and can be extended to the doped system.
Journal Article
Scaling theory for Mott-Hubbard transitions-II: quantum criticality of the doped Mott insulator
We present a T = 0 K renormalization group (RG) phase diagram for the hole-doped 2D Hubbard model on the square lattice. The RG method employed is nonperturbative in treating quantum fluctuations of the single-particle occupation number via the unitarily decoupling of one electronic state at every RG step. As a result, the RG phase diagram possesses the quantum fluctuation energy scale (ω) as one of its axes. Using effective Hamiltonians and wavefunctions for the low-energy many-body eigenstates for the doped Mott liquid obtained from the stable fixed point of the RG flows, we demonstrate the collapse of the pseudogap for charge excitations (Mottness) at a quantum critical point (QCP) possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-pseudogapping near the antinodes. The QCP is characterised using both thermodynamic and quantum information-theoretic measures. d-wave superconducting order is shown to arise from this quantum critical state of matter. The pseudogap phase possesses a variety of fluctuations that lead to several symmetry-broken phases at low-energies. Benchmarking of the ground state energy per particle and the double-occupancy fraction obtained from a finite-size scaling analysis against existing numerical results yields excellent agreement. We present detailed insight into the T = 0 origin of several experimentally observed findings in the cuprates, including Homes law and Planckian dissipation. We also establish that the heirarchy of temperature scales for the pseudogap (TPG), onset temperature for pairing (Tons), formation of the Mott liquid (TML) and superconductivity (TC) obtained from our analysis is quantitatively consistent with that observed experimentally for some members of the cuprates. Our results offer insight on the ubiquitous origin of superconductivity in doped Mott insulating states, and pave the way towards a systematic search for higher superconducting transition temperatures in such systems.
Journal Article
Distinct DNA repair pathways cause genomic instability at alternative DNA structures
Alternative DNA structure-forming sequences can stimulate mutagenesis and are enriched at mutation hotspots in human cancer genomes, implicating them in disease etiology. However, the mechanisms involved are not well characterized. Here, we discover that Z-DNA is mutagenic in yeast as well as human cells, and that the nucleotide excision repair complex, Rad10-Rad1(ERCC1-XPF), and the mismatch repair complex, Msh2-Msh3, are required for Z-DNA-induced genetic instability in yeast and human cells. Both ERCC1-XPF and MSH2-MSH3 bind to Z-DNA-forming sequences, though ERCC1-XPF recruitment to Z-DNA is dependent on MSH2-MSH3. Moreover, ERCC1-XPF
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dependent DNA strand-breaks occur near the Z-DNA-forming region in human cell extracts, and we model these interactions at the sub-molecular level. We propose a relationship in which these complexes recognize and process Z-DNA in eukaryotes, representing a mechanism of Z-DNA-induced genomic instability.
Z-DNA-forming CG repeats are mutagenic in mammalian cells but the mechanism has remained unknown so far. Here, the authors show that the nucleotide excision repair complex Rad10-Rad1 (ERCC1-XPF) and the mismatch repair complex Msh2-Msh3 (MSH2-MSH3) are required for Z-DNA-induced genetic instability in yeast and human cells.
Journal Article
Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
A
bstract
We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological Θ-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This results in a nonperturbative version of the Berezenskii-Kosterlitz-Thouless (BKT) RG phase diagram, revealing a line of intermediate coupling stable fixed points, while the nature of RG flow around the critical point is identical to that obtained from the weak-coupling RG analysis. This coincides with a phase transition in the many-particle entanglement, as the entanglement entropy RG flow shows distinct features for the critical and gapped phases depending on the value of the topological Θ-term. We demonstrate the Ryu-Takyanagi entropy bound for the many-body eigenstates comprising the EHM network, concretizing the relation to the holographic duality principle. The scaling of the entropy bound also distinguishes the gapped and gapless phases, implying the generation of very different holographic spacetimes across the critical point. Finally, we treat the Fermi surface as a quantum impurity coupled to the high energy electronic states. A thought-experiment is devised in order to study entanglement entropy generated by isolating the impurity, and propose ways by which to measure it by studying the quantum noise and higher order cumulants of the full counting statistics.
Journal Article
Mixed Contaminants: Occurrence, Interactions, Toxicity, Detection, and Remediation
The ever-increasing rate of pollution has attracted considerable interest in research. Several anthropogenic activities have diminished soil, air, and water quality and have led to complex chemical pollutants. This review aims to provide a clear idea about the latest and most prevalent pollutants such as heavy metals, PAHs, pesticides, hydrocarbons, and pharmaceuticals—their occurrence in various complex mixtures and how several environmental factors influence their interaction. The mechanism adopted by these contaminants to form the complex mixtures leading to the rise of a new class of contaminants, and thus resulting in severe threats to human health and the environment, has also been exhibited. Additionally, this review provides an in-depth idea of various in vivo, in vitro, and trending biomarkers used for risk assessment and identifies the occurrence of mixed contaminants even at very minute concentrations. Much importance has been given to remediation technologies to understand our current position in handling these contaminants and how the technologies can be improved. This paper aims to create awareness among readers about the most ubiquitous contaminants and how simple ways can be adopted to tackle the same.
Journal Article
Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) shows a violation of the area-law in real-space entanglement entropy of a subsystem, believed to be a signature of the ground state of a gapless quantum critical system of interacting fermions. Here, we apply a T = 0 renormalization group approach to the FL, unveiling the long-wavelength quantum fluctuations from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga–Luttinger liquid reveals a universal logarithmic violation of the area-law in gapless electronic liquids, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to classify the gapped quantum liquids emergent from the destabilisation of the Fermi surface by renormalisation group relevant quantum fluctuations arising from backscattering processes.
Journal Article
The Competitive Dynamics of New DVD Releases
We study the market for new (movie) DVDs in the United States. Our demand model captures seasonality, freshness (i.e., time between theatrical and DVD release), and state dependence. We also develop a structural model of dynamic competition in which studios balance waiting for high-demand weeks, against reduced freshness, and against competitive crowding. We find that studios emphasize DVD revenues from larger movies (by theatrical revenue) over DVD revenues from smaller movies. Studios also emphasize revenue from consumers who prefer larger and fresher movies. These behaviors are consistent with managerial conservatism: studio executives forgo DVD revenues from smaller movies to ensure the DVD success of larger movies.
This paper was accepted by J. Miguel Villas-Boas, marketing.
Journal Article
Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalization group analysis
We analyze the antiferromagnetic spin-1/2 XXZ model on the kagome lattice at finite external magnetic field with the help of a non-perturbative zero-temperature renormalization group (RG) technique. The exact nature of the ground and excited state properties (e.g. gapped or gapless spectrum etc) of this system are still debated. Approximate methods have typically been adopted towards understanding the low-energy spectrum. Following the work of Kumar et al (2014 Phys. Rev. B 90 174409), we use a Jordan-Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbor interactions. While the work of Kumar et al was confined mostly to the plateau at 1/3-filling (magnetization per site) in the XY regime, we analyze the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel-Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a SU(2)-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar et al. We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.
Journal Article
Assimilation, Heterolocalism and Ethnic Capital
The article examines the assimilation dynamics and functioning of ethnic organisations of a small immigrant Bengali community in the Kansas City, USA. Indian Bengalis in Overland Park (a suburban neighbourhood) formed a closely knit group and bonding social capital was sustained through activities of ethnic associations, consumption of ethnic amenities, and through weekend parties/get-togethers. Such ethnic bonding and meagre ethnic/racial diversity in the city (compared to the larger cities of the USA) are found to be contributing to slow and limited assimilation of Bengalis to the American society. These findings challenge the existing erudition that assimilation increases with improvement in socio-economic standing and suburbanisation of immigrants. Further, the article finds that assimilation there is segmental and ethnic associations not only provide a comfort zone to the immigrants in a culturally and racially different country but also play a prominent role in preserving the ethnic identity of its members.
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