Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted $XY$ universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a $2{k}_{F}$ transfer momentum, where ${k}_{F}$ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted $XY$ universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a $2{k}_{F}$ transfer momentum, where ${k}_{F}$ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.

arXiv:1606.07544Physical review. B./Physical review. BJun 16, 20171 citation

ONE-DIMENSIONAL QUANTUM SPIN LIQUIDS

P. Lecheminant

WORLD SCIENTIFIC eBooksMar 26, 20132 citations

Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions

Ribhu K. Kaul, Subir Sachdev A

We consider relativistic U(1) gauge theories in $2+1$ dimensions, with ${N}_{b}$ species of complex bosons and ${N}_{f}$ species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large ${N}_{b}$ and ${N}_{f}$ , but for arbitrary values of the ratio ${N}_{b}∕{N}_{f}$ , we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin liquids, charge liquids, and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.We consider relativistic U(1) gauge theories in $2+1$ dimensions, with ${N}_{b}$ species of complex bosons and ${N}_{f}$ species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large ${N}_{b}$ and ${N}_{f}$, but for arbitrary values of the ratio ${N}_{b}∕{N}_{f}$, we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin liquids, charge liquids, and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.

arXiv:0801.0723Physical Review BApr 3, 2008125 citations

Transition between algebraic and Z 2 quantum spin liquids at large N

Rufus Boyack, Chien-Hung Lin, Nikolai Zerf +2 more

We present a field theory description of a quantum phase transition in two spatial dimensions between a $\text{U}(1)$ algebraic spin liquid with $N$ flavors of gapless two-component Dirac fermionic spinons and a gapped ${\mathbb{Z}}_{2}$ spin liquid. This transition is driven by spinon pairing and concomitant Higgsing of the emergent U(1) gauge field. For sufficiently large $N$ , we find a quantum critical point with non-Gaussian exponents that is stable against instanton proliferation. We compute critical exponents using either $1/N$ or $\ensuremath{\epsilon}$ expansions, and give estimates of the critical value of $N$ below which the quantum critical point disappears.We present a field theory description of a quantum phase transition in two spatial dimensions between a $\text{U}(1)$ algebraic spin liquid with $N$ flavors of gapless two-component Dirac fermionic spinons and a gapped ${\mathbb{Z}}_{2}$ spin liquid. This transition is driven by spinon pairing and concomitant Higgsing of the emergent U(1) gauge field. For sufficiently large $N$, we find a quantum critical point with non-Gaussian exponents that is stable against instanton proliferation. We compute critical exponents using either $1/N$ or $\ensuremath{\epsilon}$ expansions, and give estimates of the critical value of $N$ below which the quantum critical point disappears.

arXiv:1804.00054Physical review. B./Physical review. BJul 23, 201823 citations

XY

universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a

2{k}_{F}

transfer momentum, where

{k}_{F}

is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface.

We consider relativistic U(1) gauge theories in

2+1

dimensions, with

{N}_{b}

species of complex bosons and

{N}_{f}

species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large

{N}_{b}

and

{N}_{f}

, but for arbitrary values of the ratio

{N}_{b}∕{N}_{f}

, we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin liquids, charge liquids, and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.

We present a field theory description of a quantum phase transition in two spatial dimensions between a

\text{U}(1)

algebraic spin liquid with

N

flavors of gapless two-component Dirac fermionic spinons and a gapped

{\mathbb{Z}}_{2}

spin liquid. This transition is driven by spinon pairing and concomitant Higgsing of the emergent U(1) gauge field. For sufficiently large

N

, we find a quantum critical point with non-Gaussian exponents that is stable against instanton proliferation. We compute critical exponents using either

1/N

or $\ensuremath{\epsilon}$ expansions, and give estimates of the critical value of

N

below which the quantum critical point disappears.