34,932 research outputs found
The Ricardo puzzle
This paper tackles the puzzle of Ricardo’s stubborn commitment to a labor theory of value that he himself saw as no more than an approximation to reality and which was heavily opposed by Malthus, his most respected contemporary. We show it is wrong to think that the theory had no analytical use. Quite to the contrary, it was the only defence Ricardo could find against Malthus’ destructive criticism, which introduced an unacceptable degree of indetermination in his theory of profits. By adopting the labor theory of value, Ricardo drastically simplified the method of proof of his main proposition, which otherwise seemed to present unsurmountable analytical difficulties. The irony is that the proposition was correct, quite independently of the labor theory of value, but Ricardo was just unable to prove it.
Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces
The transfer of conserved charges through insulating matter via smooth
deformations of the Hamiltonian is known as quantum adiabatic, or Thouless,
pumping. Central to this phenomenon are Hamiltonians whose insulating gap is
controlled by a multi-dimensional (usually two-dimensional) parameter space in
which paths can be defined for adiabatic changes in the Hamiltonian, i.e.,
without closing the gap. Here, we extend the concept of Thouless pumps of band
insulators by considering a larger, three-dimensional parameter space. We show
that the connectivity of this parameter space is crucial for defining quantum
pumps, demonstrating that, as opposed to the conventional two-dimensional case,
pumped quantities depend not only on the initial and final points of
Hamiltonian evolution but also on the class of the chosen path and preserved
symmetries. As such, we distinguish the scenarios of closed/open paths of
Hamiltonian evolution, finding that different closed cycles can lead to the
pumping of different quantum numbers, and that different open paths may point
to distinct scenarios for surface physics. As explicit examples, we consider
models similar to simple models used to describe topological insulators, but
with doubled degrees of freedom compared to a minimal topological insulator
model. The extra fermionic flavors from doubling allow for extra gapping
terms/adiabatic parameters - besides the usual topological mass which preserves
the topology-protecting discrete symmetries - generating an enlarged adiabatic
parameter-space. We consider cases in one and three \emph{spatial} dimensions,
and our results in three dimensions may be realized in the context of
crystalline topological insulators, as we briefly discuss.Comment: 21 pages, 7 Figure
Emergent SU(N) symmetry in disordered SO(N) spin chains
Strongly disordered spin chains invariant under the SO(N) group are shown to
display random-singlet phases with emergent SU(N) symmetry without fine tuning.
The phases with emergent SU(N) symmetry are of two kinds: one has a ground
state formed of randomly distributed singlets of strongly bound pairs of SO(N)
spins (a `mesonic' phase), while the other has a ground state composed of
singlets made out of strongly bound integer multiples of N SO(N) spins (a
`baryonic' phase). The established mechanism is general and we put forward the
cases of and as prime candidates for experimental
realizations in material compounds and cold-atoms systems. We display universal
temperature scaling and critical exponents for susceptibilities distinguishing
these phases and characterizing the enlarging of the microscopic symmetries at
low energies.Comment: 5 pages, 2 figures, Contribution to the Topical Issue "Recent
Advances in the Theory of Disordered Systems", edited by Ferenc Igl\'oi and
Heiko Riege
Highly-symmetric random one-dimensional spin models
The interplay of disorder and interactions is a challenging topic of
condensed matter physics, where correlations are crucial and exotic phases
develop. In one spatial dimension, a particularly successful method to analyze
such problems is the strong-disorder renormalization group (SDRG). This method,
which is asymptotically exact in the limit of large disorder, has been
successfully employed in the study of several phases of random magnetic chains.
Here we develop an SDRG scheme capable to provide in-depth information on a
large class of strongly disordered one-dimensional magnetic chains with a
global invariance under a generic continuous group. Our methodology can be
applied to any Lie-algebra valued spin Hamiltonian, in any representation. As
examples, we focus on the physically relevant cases of SO(N) and Sp(N)
magnetism, showing the existence of different randomness-dominated phases.
These phases display emergent SU(N) symmetry at low energies and fall in two
distinct classes, with meson-like or baryon-like characteristics. Our
methodology is here explained in detail and helps to shed light on a general
mechanism for symmetry emergence in disordered systems.Comment: 26 pages, 12 figure
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