49 research outputs found

### Topological degeneracy and pairing in a one-dimensional gas of spinless Fermions

We revisit the low energy physics of one dimensional spinless fermion
liquids, showing that with sufficiently strong interactions the conventional
Luttinger liquid can give way to a strong pairing phase. While the density
fluctuations in both phases are described by a gapless Luttinger liquid, single
fermion excitations are gapped only in the strong pairing phase. Smooth spatial
Interfaces between the two phases lead to topological degeneracies in the
ground state and low energy phonon spectrum. Using a concrete microscopic
model, with both single particle and pair hopping, we show that the strong
pairing state is established through emergence of a new low energy fermionic
mode. We characterize the two phases with numerical calculations using the
density matrix renormalization group. In particular we find enhancement of the
central charge from $c=1$ in the two Luttinger liquid phases to $c=3/2$ at the
critical point, which gives direct evidence for an emergent critical Majorana
mode. Finally, we confirm the existence of topological degeneracies in the low
energy phonon spectrum, associated with spatial interfaces between the two
phases

### Measurement-Induced Phase Transitions in the Dynamics of Entanglement

We define dynamical universality classes for many-body systems whose unitary
evolution is punctuated by projective measurements. In cases where such
measurements occur randomly at a finite rate $p$ for each degree of freedom, we
show that the system has two dynamical phases: `entangling' and
`disentangling'. The former occurs for $p$ smaller than a critical rate $p_c$,
and is characterized by volume-law entanglement in the steady-state and
`ballistic' entanglement growth after a quench. By contrast, for $p > p_c$ the
system can sustain only area-law entanglement. At $p = p_c$ the steady state is
scale-invariant and, in 1+1D, the entanglement grows logarithmically after a
quench.
To obtain a simple heuristic picture for the entangling-disentangling
transition, we first construct a toy model that describes the zeroth R\'{e}nyi
entropy in discrete time. We solve this model exactly by mapping it to an
optimization problem in classical percolation.
The generic entangling-disentangling transition can be diagnosed using the
von Neumann entropy and higher R\'{e}nyi entropies, and it shares many
qualitative features with the toy problem. We study the generic transition
numerically in quantum spin chains, and show that the phenomenology of the two
phases is similar to that of the toy model, but with distinct `quantum'
critical exponents, which we calculate numerically in $1+1$D.
We examine two different cases for the unitary dynamics: Floquet dynamics for
a nonintegrable Ising model, and random circuit dynamics. We obtain compatible
universal properties in each case, indicating that the entangling-disentangling
phase transition is generic for projectively measured many-body systems. We
discuss the significance of this transition for numerical calculations of
quantum observables in many-body systems.Comment: 17+4 pages, 16 figures; updated discussion and results for mutual
information; graphics error fixe

### Superconductivity near a ferroelectric quantum critical point in ultralow-density Dirac materials

The experimental observation of superconductivity in doped semimetals and
semiconductors, where the Fermi energy is comparable to or smaller than the
characteristic phonon frequencies, is not captured by the conventional theory.
In this paper, we propose a mechanism for superconductivity in ultralow-density
three-dimensional Dirac materials based on the proximity to a ferroelectric
quantum critical point. We derive a low-energy theory that takes into account
both the strong Coulomb interaction and the direct coupling between the
electrons and the soft phonon modes. We show that the Coulomb repulsion is
strongly screened by the lattice polarization near the critical point even in
the case of vanishing carrier density. Using a renormalization group analysis,
we demonstrate that the effective electron-electron interaction is dominantly
mediated by the transverse phonon mode. We find that the system generically
flows towards strong electron-phonon coupling. Hence, we propose a new
mechanism to simultaneously produce an attractive interaction and suppress
strong Coulomb repulsion, which does not require retardation. For comparison,
we perform same analysis for covalent crystals, where lattice polarization is
negligible. We obtain qualitatively similar results, though the screening of
the Coulomb repulsion is much weaker. We then apply our results to study
superconductivity in the low-density limit. We find strong enhancement of the
transition temperature upon approaching the quantum critical point. Finally, we
also discuss scenarios to realize a topological $p$-wave superconducting state
in covalent crystals close to the critical point

### Quantum Entanglement Growth Under Random Unitary Dynamics

Characterizing how entanglement grows with time in a many-body system, for
example after a quantum quench, is a key problem in non-equilibrium quantum
physics. We study this problem for the case of random unitary dynamics,
representing either Hamiltonian evolution with time--dependent noise or
evolution by a random quantum circuit. Our results reveal a universal structure
behind noisy entanglement growth, and also provide simple new heuristics for
the `entanglement tsunami' in Hamiltonian systems without noise. In 1D, we show
that noise causes the entanglement entropy across a cut to grow according to
the celebrated Kardar--Parisi--Zhang (KPZ) equation. The mean entanglement
grows linearly in time, while fluctuations grow like $(\text{time})^{1/3}$ and
are spatially correlated over a distance $\propto (\text{time})^{2/3}$. We
derive KPZ universal behaviour in three complementary ways, by mapping random
entanglement growth to: (i) a stochastic model of a growing surface; (ii) a
`minimal cut' picture, reminiscent of the Ryu--Takayanagi formula in
holography; and (iii) a hydrodynamic problem involving the dynamical spreading
of operators. We demonstrate KPZ universality in 1D numerically using
simulations of random unitary circuits. Importantly, the leading order time
dependence of the entropy is deterministic even in the presence of noise,
allowing us to propose a simple `minimal cut' picture for the entanglement
growth of generic Hamiltonians, even without noise, in arbitrary
dimensionality. We clarify the meaning of the `velocity' of entanglement growth
in the 1D `entanglement tsunami'. We show that in higher dimensions, noisy
entanglement evolution maps to the well-studied problem of pinning of a
membrane or domain wall by disorder

### Dynamics of entanglement and transport in 1D systems with quenched randomness

Quenched randomness can have a dramatic effect on the dynamics of isolated 1D
quantum many-body systems, even for systems that thermalize. This is because
transport, entanglement, and operator spreading can be hindered by `Griffiths'
rare regions which locally resemble the many-body-localized phase and thus act
as weak links. We propose coarse-grained models for entanglement growth and for
the spreading of quantum operators in the presence of such weak links. We also
examine entanglement growth across a single weak link numerically. We show that
these weak links have a stronger effect on entanglement growth than previously
assumed: entanglement growth is sub-ballistic whenever such weak links have a
power-law probability distribution at low couplings, i.e. throughout the entire
thermal Griffiths phase. We argue that the probability distribution of the
entanglement entropy across a cut can be understood from a simple picture in
terms of a classical surface growth model. Surprisingly, the four length scales
associated with (i) production of entanglement, (ii) spreading of conserved
quantities, (iii) spreading of operators, and (iv) the width of the `front' of
a spreading operator, are characterized by dynamical exponents that in general
are all distinct. Our numerical analysis of entanglement growth between weakly
coupled systems may be of independent interest.Comment: 17 pages, 16 figure